Personal Finance - Investing Money



Personal Finance - Investing Money

Compound Interest

Most investments earn compound interest. This means that at the end of each interest period the earned interest is added to the principal. The formula used to calculate the future or accumulated amount, A, is:

A = P(1 + r/n)nt

Where, P is the present amount or principal;

r is the interest rate per compounding period expressed as a decimal;

n is the total number of compounding periods per year;

t is the number of years

Common compounding periods are:

Annual: 1 time per year

Semi-annual: 2 times a year, or every 6 months

Quarterly: 4 times a year, or every 3 months

Monthly: 12 times a year, or every month

Daily: 365 times a year, or every day

For Example:

For an investment of $500 at 8% per annum, compounded annually, for 3 years,

P = ________, r = _____, n = _____, and t = ______.

A = ______(1 + ____/____)____*____

= ________________

For an investment of $1500 at 6% per annum, compounded quarterly, for 5 years,

P = ________, r = ______, n = _____, and t = _____.

A = ______(1 + ____/____)____*____

= _______________

Rule of 72

The Rule of 72 can be used to estimate the time, t, in years, needed for an investment to double in value at a given annual interest rate.

t = _________72________

Annual Interest Rate

For Example:

How long will it take for an investment to double its’ value at 4% per annum.

How long will it take for an investment to double its’ value at 12% per annum.

TVM Solver

To access TVM Solver, go to the APPS menu(Finance on the TI-83) to solve for the future value of an investment. You will need to enter the following values:

N = total number of payments

I% = annual interest rate as a percent

PV = present value(a negative amount indicates the amount is

invested)

PMT = payment each period

FV = future value, or accumulated amount

P/Y = number of payments per year

C/Y = number of compounding periods per year

PMT: END BEGIN when in the month payments will be made

Place the cursor beside FV = and press ALPHA ENTER to find what the investment will be worth.

For Example:

If you decide to invest $10 000 in a bank that offers an interest rate of 6.25% compounded annually, what will your money be worth in 5 years if the interest rate remains unchanged?

N =

I% =

PV =

PMT =

FV =

P/Y =

C/Y =

PMT: END BEGIN

Extra Examples:

1. Using the compound interest formula A = P(1 + r/n)nt , determine the future amount and the interest earned for each of the following investments. In each case, A represents the future amount after time, t, years; P represents the principal; r represents the interest rate per annum expressed as a decimal; and n represents the number of compounding periods per year.

a) An amount of $1000 is invested at 6% per annum, compounded semi-annually, for 5 years.

b) An amount of $800 is invested at 4.8% per annum, compounded

semi-annually, for 3 years.

c) An amount of $600 is invested at 8% per annum, compounded quarterly, for 3 years.

d) An amount of $1200 is invested at 6.8% per annum, compounded quarterly, for 10 years.

e) An amount of $2500 is invested at 12% per annum, compounded monthly, for 4 years.

f) An amount of $10 000 is invested at 5.4% per annum, compounded monthly, for 8 years.

2. Using the TVM Solver, compare the following pairs of investments over a 2-year period. In each case, determine the future value of each investment and state which option is the better choice.

a) A bank offers an interest rate of 10% p.a., compounded monthly.

Option 1: Invest $2400 at the beginning of each year.

N = FV =

I% = P/Y =

PV = C/Y =

PMT = PMT: END BEGIN

Option 2: Invest $200 at the beginning of each month.

N = FV =

I% = P/Y =

PV = C/Y =

PMT = PMT: END BEGIN

Option 1 or Option 2?

b) A bank offers an interest rate of 5.7% p.a., compounded quarterly.

Option 1: Invest $4000 at the beginning of each year.

N = FV =

I% = P/Y =

PV = C/Y =

PMT = PMT: END BEGIN

Option 2: Invest $1000 at the beginning of each quarter.

N = FV =

I% = P/Y =

PV = C/Y =

PMT = PMT: END BEGIN

Option 1 or Option 2?

2. Continued.

c) A bank offers an interest rate of 6.8% p.a., compounded semi-annually.

Option 1: Invest $1000 at the beginning of each year.

N = FV =

I% = P/Y =

PV = C/Y =

PMT = PMT: END BEGIN

Option 2: Invest $500 at the beginning of each 6-month period.

N = FV =

I% = P/Y =

PV = C/Y =

PMT = PMT: END BEGIN

Option 1 or Option 2?

d) Option 1: Invest $2000 at 8.5% p.a., compounded monthly.

N = FV =

I% = P/Y =

PV = C/Y =

PMT = PMT: END BEGIN

Option 2: Invest $2000 at 8.55% p.a., compounded semi-annually.

N = FV =

I% = P/Y =

PV = C/Y =

PMT = PMT: END BEGIN

Option 1 or Option 2?

3. a) A bank offers an interest rate of 6.5% p.a., compounded monthly.

How many years will it take for an investment of $1000 to be worth $1200?

N =

I% =

PV =

PMT =

FV =

P/Y =

C/Y =

PMT: END BEGIN

b) A bank offers an interest rate of 6.5% p.a., compounded monthly. If $35 is invested at the beginning of each month, how many years will it take for the investment to be worth $1200?

N =

I% =

PV =

PMT =

FV =

P/Y =

C/Y =

PMT: END BEGIN

Personal Finance - Investing for the Future- #1 Name:__________

• When you invest your money, the interest you receive on your investment is taxed each year.

• However, if you qualify and invest in a registered retirement savings plan(RRSP), you can defer the tax that you must pay on both the principal and any interest earned.

• The tax which you defer by having an RRSP is usually not collected until you retire. At that time, your income will be much less¸ and your tax rate will also be much less.

• The Marginal Tax Rate of income tax is the rate charged on the last(greatest) dollar earned. As your income increases, the rate of tax you pay increases. Sometimes this is referred to as your tax bracket.

• Examples of Taxable Income:__________________________________

________________________________________________________________

________________________________________________________________

________________________________________________________________

• Examples of Deductions from Taxable Income:___________________

________________________________________________________________

________________________________________________________________

________________________________________________________________

For Example:

Mary paid a total of $26 000 tax on her $81 000 salary. She received a final bonus of $1000, and paid $450 tax on these last thousand dollars This means that her marginal tax rate is $450 per $1000, or 45%. Therefore, if she buys an RRSP for that last $1000, she will receive a tax refund of $450, thus saving 45%

More Examples:

1. A $4500 RRSP is purchased. Calculate the tax rebate for each of the following marginal tax rates.

a) 34% b) 39% c) 45% d) 22%

2. For each of the following non-registered savings plans, calculate the income tax payable at the end of the first year.

a) an investment of $1000 at 5.5% p.a., compounded annually, with a marginal tax rate of 25%

b) an investment of $2500 at 6.2% p.a., compounded annually, with a marginal tax rate of 39%

c) an investment of $3000 at 6.4% p.a., compounded semi-annually, with a marginal tax rate of 44%

3. Using the formulas below, calculate the average annual rate of return for each of the following investments.

Average Annual Return = Total Return / Number of Years

Average Annual Rate of Return = Average Annual Return / Original Investment

a) Total Return =$18 620, Investment =$20 000, Number of Years =10

b) Total Return =$65 800, Investment =$15 000, Number of Years =25

c) Total Return = $28 680, Investment = $10 000, Number of Years = 20

4. Using the formulas given in exercise 5 and the formula:

Total Return = Closing Balance – Tax Paid – Original Investment,

complete the table below for each of the following investments.

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5. Consumers often choose not to reinvest their tax rebate but to spend it instead.

a) Using the TVM solver, determine the closing balance for a $2000 RRSP at 6.5% p.a., compounded annually, for 30 years. Assume that there is no reinvestment of the tax rebate.

b) Calculate the average annual rate of return for this investment if the marginal tax rate is 44%.

6. At age 18, you purchase a $500 RRSP at 6% p.a., compounded annually. Your marginal tax rate is 30%. You choose not to reinvest your tax rebate.

a) What will your closing balance be at age 60?

b) How much tax will you have to pay if you decide to withdraw the entire amount at age 60?

c) What will be the total return on your investment, assuming that you withdraw the entire amount at age 60?

d) Calculate the average annual rate of return for this investment.

7. Using the TVM Solver, determine the closing balance for each of the following RRSP investments, assuming that the tax rebates are not reinvested.

a) An amount of $200 is invested at the end of each 3-month period at 5.8% p.a., compounded quarterly, from age 20 to age 55.

b) An amount of $500 is invested at the end of each 6-month period at 6.4% p.a., compounded semi-annually, from age 25 to age 65.

c) An amount of $50 is invested at the end of every month at 7.1% p.a., compounded annually, for 30 years.

8. Using the TVM Solver, determine the following regarding RRSP investments. Assume that the tax rebates are not reinvested.

a) How many years will it take for an investment of $500 paid at the end of every month at 6% p.a., compounded monthly, to be worth $1 000 000?

b) How many years will it take for an investment of $500 paid at the end of every month at 12% p.a., compounded monthly, to be worth $1 000 000?

c) How many years will it take for an investment of $200 paid at the end of every month at 9.5% p.a., compounded monthly, to be worth $250 000?

9. Using the TVM Solver, determine the following regarding RRSP investments. Assume that the tax rebates are not reinvested.

a) What amount of money must be invested monthly from ages 20 to 55 at 8.5% p.a., compounded monthly, in order to accumulate $1 000 000?

b) What amount of money must be invested quarterly from ages 20 to 60 at 6.4% p.a., compounded quarterly, in order to accumulate $500 000?

10. From the day you are born, your parents invest $50 at the end of every month at 6.8% p.a., compounded monthly, into a non-taxable Registered Education Savings Plan for your college education. Using the TVM Solver, calculate how much money will have accumulated by the time you reach age 18.

Registered Retired Savings Plans versus Non-Registered Investments

Brian and his 35 year old twin brother Darcy are trying to decide how to best save for their retirement. Both brothers work as firemen earning about $60,000 per year, thus their marginal tax rate is 38%. Brian decides to invest $2,000 in a Mutual Fund as an R.R.S.P. while Darcy decides to invest $2,000 in the same Mutual Fund but not register it. They are then going to invest $100 monthly until they both retire at 55. The mutual fund has on average been earning 7% interest per year compounded quarterly. At fifty five, they will be living on their firemen’s pension of $30,000 per year plus they will start drawing on their investments. At that income their marginal tax rate will be 16%. Who will be doing better?

| |Brian |Darcy |

|Initial Investment | | |

| | | |

|Initial Tax Refund | | |

| | | |

|Yearly Tax Refund | | |

| | | |

|Yearly Tax Payments | | |

| | | |

|Value of Investment at | | |

|Retirement | | |

|Total Tax Payments | | |

| | | |

|Total Tax | | |

|Refunds | | |

| | | |

|Interest at Retirement | | |

| | | |

|Taxes at Retirement | | |

| | | |

| | | |

|Totals | | |

Personal Finance - Investment Portfolios

1. Using the table of investment strategies for various life stages found on page 167 of the Source Book, determine the recommended allocations to cash, equities and income for each of the following people.

a) Mary, a 70-year old retiree, plans to invest $1200.

b) Elizabeth, a 48-year old biologist, plans to invest $6000.

c) John, a 58-year old teacher, plans to invest $8000.

d) Sam, a 22-year old aircraft technician, plans to invest $3000.

2. Find the effective annual interest rate for each of the following nominal rates of interest.

a) 6.5% per annum, compounded monthly

b) 4.8% per annum, compounded daily

c) 7.1% per annum, compounded quarterly

d) 5.4% per annum, compounded semi-annually

3. Compare the following pairs of interest rates by calculating the effective annual interest rate for each. For each pair, state which interest rate is the better one.

a) A: 6.2% monthly B: 6.25% annually

b) A: 8% quarterly B: 8.1% semi-annually

c) A: 10.75% daily B: 11% monthly

d) A: 22.25% quarterly B: 22.5% semi-annually

4. Calculate the total return and the average annual rate of return for the following investment portfolio. Ignore taxes.

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5. Calculate the total return and the average annual rate of return for the following investment portfolio. Ignore taxes.

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6. On February 1, 1998, $8000 was invested in a GIC at 6.8% p.a., compounded semi-annually.

a) What will the GIC be worth on February 1, 2002?

b) What is the average annual rate of return over the period of this investment?

7. An amount of $12 000 is invested in a GIC at 8.5% p.a., compounded annually. Calculate the future value and the average annual rate of return for this investment for each of the following time periods.

a) 5 years b) 10 years c) 30 years

8. An investment of $20 000 is held from February 1, 1990, to February 1, 2000. Canadian stocks that track the TSE 300 index are 60% of the portfolio. Bonds that pay 6.5%, compounded annually, are 20% of the portfolio, and the remaining 20% of the portfolio is invested in mutual funds that yield a return of 15.8% per year. On February 1, 1990, the TSE 300 index was at 4568. On February 1, 2000, the TSE 300 index was at 6876.

a) What was the value of the total portfolio on February 1, 2000?

b) What average annual rate of return does the value in part a

represent?

9. Complete the following table tracking the annual closing balance of a $20 000 mutual fund over a 5-year period. What is the average annual rate of return over the 5-year period? (Note: The use of brackets in 1999 indicates that the fund lost money.)

[pic]

10. Copy the following table and calculate the average annual rate of return for each of the following investments.

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11. Complete the following table tracking the annual closing balance of a $12 000 mutual fund over a 5-year period. Determine the closing balance in 1999, the total return on the investment after 5 years, and the average annual rate of return for this period. (Note: The use of brackets in 1998 and 1999 indicates that the fund lost money.)

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Leasing

When you lease an item, you make monthly payments to cover the depreciation of the item over the duration of the lease, taxes on the amount of the depreciation, and interest on the outstanding balance of the full purchase price.

The price of a lease depends on three factors: the residual value, the interest rate offered for the lease, and the length of the lease. Down payments may also effect the lease.

Residual Value:_________________________________________________________

______________________________________________________________________

______________________________________________________________________

Depreciation:___________________________________________________________

______________________________________________________________________

______________________________________________________________________

Interest Rate:___________________________________________________________

______________________________________________________________________

______________________________________________________________________

1. Using the chart on page 174 of the Source Book, complete the table below for a sport utility vehicle with a purchase price of $38 000.

Depreciation .70 .64 .60 .55 .48

2. There are 2 ways in which you can own a car after 3 years. You can purchase the car now or lease the car for 3 years and then purchase it. Consider a new car with a purchase price of $18 500 plus taxes.

Using the TVM solver, examine the following two options.

Option 1: Purchase. There is a down payment of $8000. GST is 5% and PST is 7%. The car is purchased with a loan of 1.9% p.a., compounded semi-annually, and paid monthly for 3 years. Determine the following.

a) What is the total cost of the car, including taxes?

b) What is the total amount to be borrowed?

c) What is the monthly payment on the loan?

d) What is the total amount paid for the car, including the down payment?

Option 2: Lease and Purchase. There is no down payment. The lease payment is $325 per month, plus GST and PST. After 3 years, you purchase the car for $7500, plus GST and PST. GST is 5% and PST are each 7%. Determine the following.

a) What is the monthly lease payment, including taxes?

b) What is the total of the lease payments over the 3-year period?

c) What is the total amount paid for the car after the purchase?

3. A new car with a purchase price of $46 500 can be either purchased outright or leased and then purchased. There is 5% GST and no PST. Consider the following options.

Option 1: Purchase. There is a down payment of $12 000. The car is purchased with a loan of 0.9% p.a., compounded semi-annually, and paid monthly for 4 years. Determine the following.

a) What is the total cost of the car, including taxes?

b) What is the total amount to be borrowed?

c) What is the monthly payment on the loan?

d) What is the total amount paid for the car, including the down payment?

Option 2: Lease and Purchase. There is a down payment of $8000. The lease payment is $450 per month, plus GST. After 4 years, the car is purchased for $18 500, plus GST. Determine the following.

a) What is the monthly lease payment, including taxes?

b) What is the total of the lease payments over the 4-year period?

c) What is the total amount paid for the car after purchase, including the down payment?

4. A new car with a purchase price of $22 600 can be either purchased outright or leased and then purchased. There is 5% GST and 7% PST. Consider the following options.

Option 1: Purchase. There is a down payment of $10 000. The car is purchased with a loan of 1.5% p.a., compounded semi-annually, and paid monthly for 2 years. Determine the following.

a) What is the total cost of the car, including taxes?

b) What is the total amount to be borrowed?

c) What is the monthly payment on the loan?

d) What is the total amount paid for the car, including the down payment?

Option 2: Lease and Purchase. There is a down payment of $5000. The lease payment is $350 per month, plus taxes. After 2 years, the car is purchased for $12 400, plus taxes. Determine the following.

a) What is the monthly lease payment, including taxes?

b) What is the total of the lease payments over the 2-year period?

c) What is the total amount paid for the car after purchase, including the down payment?

d) The purchaser decides to take out a 2-year bank loan for the purchase price of $12 400. The bank offers an interest rate of 7.5% p.a., compounded semi-annually. Calculate the total amount paid for the car after purchase if the purchase price is financed through the bank.

5. Using the TVM solver, calculate the lease-end value for each of the following. Taxes are already included in the purchase prices.

a) A vehicle with a purchase price of $12 500 is leased for $185.50 per month, including taxes, at an interest rate of 4.5% p.a., compounded monthly, over 4 years.

b) A vehicle with a purchase price of $25 800 is leased for $460.00 per month, including taxes, at an interest rate of 3.2% p.a., compounded monthly, over 3 years.

c) A vehicle with a purchase price of $32 650 is leased for $625.00 per month, including taxes, at an interest rate of 2.8% p.a., compounded monthly, over 2 years.

6. Using the TVM solver, calculate the monthly lease payment, before taxes, for each of the following.

a) A car with a purchase price, including taxes, of $32 655.60 is leased for 3 years with a lease-end value of $14 650 and an interest rate of 1.8% p.a., compounded monthly. There is no down payment.

b) A car with a purchase price, including taxes, of $26 825.20 is leased for 2 years with a lease-end value of $14 650 and an interest rate of 3.2% p.a., compounded monthly. There is a down payment of $8000.

c) A car with a purchase price, including taxes, of $48 205.30 is leased for 4 years with a lease-end value of $18 318.00 and an interest rate of 1.9% p.a., compounded monthly. There is a down payment of $12 000.

7. Complete the following table in order to determine the total leasing cost and the lease-end value of a vehicle with a purchase price of $23 550.25, including taxes.

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The monthly lease payment is equal to the base monthly lease payment plus taxes of 12%. The security deposit is equal to one monthly payment, rounded up to the nearest $25. The total due upon signing is equal to the sum of the down payment, the first month’s lease payment, the security deposit, and the filing fee. The total lease cost is equal to the sum of the down payment, the total of all lease payments (less the security deposit), and the filing fee.

Mortgages

Mortgage:______________________________________________________________

______________________________________________________________________

Principal:______________________________________________________________

______________________________________________________________________

Interest:_______________________________________________________________

_____________________________________________________________________

Mortgage Payment:______________________________________________________

______________________________________________________________________

Amortization Period:_____________________________________________________

______________________________________________________________________

Term:_________________________________________________________________

______________________________________________________________________

______________________________________________________________________

Gross Debt Service Ratio:_________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

Actual Monthly Mortgage Payment + Monthly Property Taxes + Monthly Heating X 100 = GDS

Gross Monthly Income

1. Determine the maximum house payment that should be considered for each of the following incomes. Assume that the total monthly house payment should not exceed 27% to 32% of the total gross monthly income.

a) Toby earns $25.50 an hour. He works 40 h a week.

b) Nell works an average of 48 h a week. She earns $55.25 an hour for the first 40 h per week and time and a half for each additional hour.

c) Ben has an annual salary of $65 780.00.

d) Jergen earns $38.50 an hour and works 37 h a week. His wife, Lara, earns $45.75 an hour and works 30 h a week.

2. Using TVM solver, determine the monthly mortgage payment for a mortgage of $75 000 at 8% p.a., compounded semi-annually, for each of the following amortization periods.

(i) 25 years (ii) 20 years (iii) 15 years

3. Using TVM solver, determine the mortgage amount for each of the following. Assume that you are compounding monthly for each question.

a) a monthly mortgage payment of $1257 at an interest rate of 7.25%, amortized over 15 years

b) a monthly mortgage payment of $1478 at an interest rate of 6.50%, amortized over 25 years

a) a monthly mortgage payment of $2024 at an interest rate of 6.00%, amortized over 20 years

4. Calculate the total amount paid for each of the following mortgages.

a) A monthly payment of $1234 is paid over a period of 25 years.

b) A monthly payment of $1025 is paid over a period of 15 years.

c) A monthly payment of $985 is paid over a period of 20 years.

5. Using the TVM solver, determine the monthly payment, the total amount paid, and the total interest paid for each of the following mortgages.

a) A mortgage of $80 000 at 7.2% p.a., compounded semi-annually, is amortized over 25 years and paid monthly.

b) A mortgage of $120 000 at 8.25% p.a., compounded semiannually, is amortized over 20 years and paid monthly.

c) A mortgage of $100 000 at 6.25% p.a., compounded semiannually, is amortized over 15 years and paid monthly.

d) A mortgage of $100 000 at 6.25% p.a., compounded semiannually, is amortized over 15 years and paid bi-weekly.

e) A mortgage of $120 000 at 8.5% p.a., compounded semi-annually, is amortized over 10 years and paid bi-weekly.

6. How much will still be owing on the mortgages in exercise 5 after 5 years? after 10 years?

7. How much will be saved on a mortgage of $120 000 at 7.5% p.a., compounded semi-annually, and amortized over 25 years if payments are made bi-weekly instead of monthly?

8. How much will be saved on a mortgage of $120 000, paid monthly over 25 years, if the interest rate is 7.0% p.a., compounded semiannually, instead of 7.5% p.a., compounded semi-annually?

9. How much will be saved on a mortgage of $120 000 paid monthly at 7.5% p.a., compounded semi-annually, if the amortization period is 20 years instead of 25 years?

10. How much will be saved on a mortgage of $120 000 paid monthly at 7.5% p.a., compounded semi-annually, if the amortization period is 10 years instead of 25 years?

11. A couple purchase a new home. Their mortgage of $90 000 is amortized over 25 years with a 3-year term at a fixed interest rate of 7% p.a., compounded monthly.

a) What will the monthly payment be?

b) How much will be owed on the mortgage at the end of the 3 years?

c) At the end of the 3 years, the interest rate will increase by 2% per annum. What will their new monthly payment be if the mortgage is amortized over the remaining 22 years?

13. David and Gina make monthly payments on a mortgage of $100 000 at 7.25% p.a., compounded semi-annually, and amortized over 25 years. The interest rate is fixed for a 2-year term and will have to be re-negotiated after this period.

a) What is their monthly mortgage payment?

b) How much will be owed on the mortgage at the end of the 2 years?

c) They re-negotiate a 5-year mortgage to be paid monthly at 7.0% p.a., compounded semi-annually, and amortized over 23 years. What will their new monthly mortgage payment be?

d) How much will be owed on the mortgage at the end of this 5-year period?

14. Andrew and Elizabeth make monthly payments on a mortgage of $ 98 000 at 6.25% p.a., compounded semi-annually, and amortized over 10 years. The interest rate is fixed for a 5-year term and will have to be re-negotiated at the end of this period.

a) What is their monthly mortgage payment?

b) How much will be owed on the mortgage at the end of the 5 years?

c) What is the total amount paid over this 5-year period?

d) They re-negotiate their mortgage at an interest rate of 7.5% p.a., compounded semi-annually, and amortized over 5-years. They decide to make bi-weekly payments. What is their bi-weekly mortgage payment?

e) How much will they have paid over the 10 years that they have had their mortgage?

f) How much interest will they have paid over the 10 years?

Renting Versus Buying

1. Linda owns a home valued at $145 000. She has a monthly mortgage payment of $985.45.

a) For tax purposes, the assessed value is 75% of the fair market value, and the tax rate is 20 mills. Calculate her annual property tax bill. How much money must be set aside each month in order to pay the property tax?

b) Her estimated household expenses are summarized in the following table. Calculate her average monthly household expenses.

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c) Calculate Linda’s average monthly cost for her home.

2. Steve and Annie rent a home for $1200 a month, not including the cost of utilities. Their estimated utility costs are summarized below.

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Calculate Steve and Annie’s average monthly cost for rent and utilities.

3. Rachel and Mordechai have a mortgage of $120 000 at 7.25% p.a., compounded semi-annually, and amortized over 15 years. The assessed value of their home is $185 000 and the tax rate is 12.8 mills. Their estimated household expenses are summarized below.

[pic]

Calculate Rachel and Mordechai’s average monthly cost for their home.

4. The current value of a home is $180 000. There is a mortgage on the home for $130 000 at 7.5% p.a., compounded semi-annually, and amortized over 25 years. The value of the home increases by 3% per year.

a) What is the value of the home after 5 years?

b) How much is still owed on the home after 5 years?

c) Determine the equity in the home after 5 years.

5. The current value of a home is $230 000. There is a mortgage on the home for $200 000 at 6.75% p.a., compounded semi-annually, and amortized over 15 years. The value of the home increases by 2% per year.

a) What is the value of the home after 10 years?

b) How much is still owed on the home after 10 years?

c) Determine the equity in the home after 10 years.

6. Vinay has saved $15 000 for a down payment on a home. He decides to invest this money at 12.5% p.a., compounded annually, for 5 years and rent an apartment for $750 a month during this time. He also plans to save $500 a month which he will invest at 8% p.a., compounded monthly.

a) How much rent will Vinay have paid over the 5 years?

b) How much will his investment of $15 000 be worth after 5 years?

c) How much will his investment of $500 a month be worth after 5 years?

d) Is this a wise decision if he wants to save more money for the down payment before he purchases a home? Give figures to support your answer.

e) If he is only able to save $300 a month, will this still be a wise decision? Explain.

7. A home can be purchased for $150 000 with a down payment of $25 000. A mortgage can be obtained at 7% p.a., compounded semiannually, and amortized over 15 years. Taxes, maintenance and insurance are estimated to be $3800 per year. The value of the home increases by 2% per year. A similar home can be rented for $1000 a month and the $25 000 down payment invested in an RRSP at 5.8% p.a., compounded annually. There are no taxes, maintenance, or insurance payments on this rental.

Complete the table below to compare the purchase of the home with the rental of a similar home. Determine the balance for each option after a 5-year period.

[pic]

8. The home in exercise 7 is paid off over 15 years.

a) Determine the following, assuming that the home is purchased.

(i) What is the total amount paid over the 15 years, including the down payment?

(ii) What is the value of the home after 15 years?

(iii) What is the equity in the home after 15 years?

(iv) What is the balance after this 15-year period?

b) Determine the following, assuming that a similar home is rented.

(i) What is the total paid for rent over the 15 years?

(ii) What is the investment of $25 000 worth after 15 years?

(iii) What is the balance after this 15-year period?

9. Using the RENTBUY spreadsheet, analyze both the option to purchase a home and the option to rent a similar home. Assume that the annual inflation for rent, utilities and maintenance averages 3.5%. The home will be paid off over 15 years. The rental will be for a 15-year period.

PURCHASING:

Cost of Home: $204 000

Down payment: $20 000

Mortgage rate: 7.5% p.a., compounded semi-annually, over 15 years and paid monthly

Insurance: $1200 annually

Property Tax: $1850 annually

Maintenance: $100 monthly

Hydro: $85.00 monthly

Water: $35.00 monthly

Gas: $65.00 monthly

Average appreciation on home: 2.5% annually

RENTING:

Rent: $1050 monthly

Invest the down payment in an RRSP at 6% p.a., compounded annually, for 15 years

Rental Insurance: $35.00 monthly

Hydro: $85.00 monthly

Water: $35.00 monthly

Gas: $65.00 monthly

10. How would the analysis in exercise 10 change if the amortization period of the mortgage and the investment period of the down payment were both 20 years?

Maximum Affordable House

There are two ways to buy a home or condominium:

1. Go to a bank and have a loans officer discuss your finances, and then come up with a pre-approved purchase/mortgage amount based on your income and probable household expenses. You then go house hunting, looking for homes in that price range.

Or

2. You go house hunting, and find something that you would like to buy. You then go to your bank and apply for a mortgage based on the purchase price of the home, your income and probable household expenses. Your application may be accepted or declined depending on your financial situation.

For Example:

The Mazur’s are a newly married couple who wish to purchase a condominium. The couple has a gross monthly income of $2800. They are able to make a down payment of $15,000 towards the purchase of their condominium.

The couple takes out a fixed-rate mortgage for the remaining amount. They are interested in amortizing their mortgage over a 25 year period. After checking various financial institutions, they find one that offers them a rate of 6.5%.

They estimate their monthly property taxes to be about $165 and their heating costs to be about $70. They expect their monthly condo fees to be $300.

Method 1: How much can they actually afford?

Gross monthly household income: ________________

Multiply: (Gross Debt Service ratio) x 0.32

Total affordable household expenses = ________________

Subtract:

Monthly property taxes - ________________

Monthly heating costs - ________________

½ if condo/strata fees (if applicable) - ________________

Monthly affordable mortgage payment = ________________

Divide: Interest Rate Factor(next page) [pic] ________________

Maximum Amount of affordable mortgage = ________________

Add: cash down payment + ________________

Maximum affordable home price = ________________

They find a condo that costs $115 000. Using the same financial information as above, will their mortgage application be accepted or denied?

Method 2: Can they afford a particular home/condo?

Actual mortgage payment

= interest rate factor x actual total mortgage = ________________

Gross debt service ratio

= actual monthly mortgage payment + property taxes + heating

gross monthly income

= ________________

Interest Rate Factor Table

Rate Factor Rate Factor Rate Factor

6.0% 0.00640 8.0% 0.00763 10.0% 0.00894

6.5% 0.00670 8.5% 0.00795 10.5% 0.00928

7.0% 0.00700 9.0% 0.00828 11.0% 0.00963

7.5% 0.00732 9.5% 0.00861 11.5% 0.00997

Maximum Affordable House

Amelia decided to buy a house worth $95,000.00. The down payment will be $8000.00, the monthly property taxes are $120.00 and the heating costs are $110.00 per month. Using the following chart, calculate the maximum affordable price, the monthly mortgage payment, and the gross debt ratio if the bank will finance the house at 7.50% for 25 years. Her gross monthly income is $2600.00.

Gross monthly household income: ________________

Multiply: (Gross Debt Service ratio) x 0.32

Total affordable household expenses = ________________

Subtract:

Monthly property taxes - ________________

Monthly heating costs - ________________

Monthly affordable mortgage payment = ________________

Divide: Interest Rate Factor [pic] ________________

Maximum Amount of affordable mortgage = ________________

Add: cash down payment + ________________

Maximum affordable home price = ________________

Actual mortgage payment

= interest rate factor x actual total mortgage = ________________

Gross debt service ratio

= actual monthly mortgage payment + property taxes + heating

gross monthly income

= ________________

Interest Rate Factor Table

Rate Factor Rate Factor Rate Factor

6.0% 0.00640 8.0% 0.00763 10.0% 0.00894

6.5% 0.00670 8.5% 0.00795 10.5% 0.00928

7.0% 0.00700 9.0% 0.00828 11.0% 0.00963

7.5% 0.00732 9.5% 0.00861 11.5% 0.00997

Net Worth

When going to a financial advisor, investment counselor, or a bank manager to apply for a loan, they will ask you to do a Net Worth Statement. It calculates the difference between your total assets or what you own, and your total liabilities or what your owe.

Your assets are divided into 3 categories:

Liquid Assets are assets that you can quickly convert into cash in the case of an emergency or investment opportunity. Eg.: savings and chequing accounts, short-term deposits, Canada Savings Bonds, etc.

Every individual should have an emergency fund containing liquid assets that equal about 3 to 6 months of employment income.

Semi-Liquid Assets include longer-term investments that you can use for a major future need such as education or retirement. These include stocks, bonds other real estate property, and retirement funds such as RRSP’s.

Non-Liquid Assets are personal assets that you acquire for your own long term use or enjoyment such as homes, cottages, cars, boats, and furniture. Their value can be used as collateral in applying for a loan.

Your liabilities are divided into 2 categories:

Short-term debts are debts you must repay within a twelve-month period. These include credit card balances, personal and consumer loans, installments, and taxes.

Long term debts are all debts other than those you must pay within a year. These include home and cottage mortgages, home renovation loans, real estate loans and mutual funds.

One of the most important ratios used to analyze a net worth statement is the Debt/Equity Ratio. This compares all debt excluding the mortgage on your home to the equity or net worth. This ratio should never exceed 50% which means that an individuals debt burden is too high and should be reduced.

The formula for calculating the Debt/Equity Ratio is:

Debt/Equity Ratio = Total Liabilities - Mortgage x 100

Net Worth

For Example:

Prepare a net worth statement for Olivia Jones. Olivia has $670 in her chequing account and $1500 in a savings account. Her life insurance policy has a $5000 cash surrender value. She has $6000 invested in mutual funds and $35,000 in a registered pension plan. Her home is valued at $85,000 on which she has an outstanding mortgage of $62,000. Her car is valued at $18,000. She has a car loan of $8,000 that must be repaid within 2 years. The balance owing on her credit cards is $495.

Statement of Net Worth

Assets(What you own)

1. Liquid/Current Assets

i. Bank accounts _______________

ii. Near Cash _______________

TOTAL Liquid Assets _______________

2. Semi-Liquid Assets

i. Mutual Funds _______________

ii. Stocks/Bonds _______________

iii. RRSPs _______________

iv. RPPs _______________

TOTAL Semi-Liquid Assets _______________

3. Non-Liquid Assets

i. Principal Residence _______________

ii. Vehicles _______________

iii. Other _______________

TOTAL Non-Liquid Assets _______________

TOTAL ASSETS _______________

Liabilities(What you owe)

4. Short-Term Debt

i. Credit card debt _______________

ii. Short-term loans _______________

TOTAL Short-Term Debt _______________

5. Long-Term Debt

i. Mortgage ______________

ii. Other ______________

TOTAL Long-Term Debt _______________

TOTAL LIABILITIES _______________

NET WORTH

(Total Assets - Total Liabilities) _______________

DEBT-EQUITY RATIO Total Liabilities - Mortgage x 100

Net Worth _______________

For Example:

Prepare a net worth statement for Melody Walters using the net worth statement which follows.

• Melody has $1435 in a chequing account and $3800 in a savings account.

• She has $6000 in Canada Savings Bonds and $5000 in a Money Market Fund.

• Her life insurance has a $2600 cash surrender value.

• Melody has $18,000 invested in bonds and $48,000 in a registered retirement pension plan.

• Melody’s condominium is valued at $85,500 with an outstanding mortgage of $52,000.

• She also owns her car valued at $17,900.

• She owes $856 on her credit cards and has a short term personal loan of $2800.

Statement of Net Worth

Assets(What you own)

1. Liquid/Current Assets

iii. Bank accounts _______________

iv. Near Cash _______________

TOTAL Liquid Assets _______________

2. Semi-Liquid Assets

v. Mutual Funds _______________

vi. Stocks/Bonds _______________

vii. RRSPs _______________

viii. RPPs _______________

TOTAL Semi-Liquid Assets _______________

3. Non-Liquid Assets

iv. Principal Residence _______________

v. Vehicles _______________

vi. Other _______________

TOTAL Non-Liquid Assets _______________

TOTAL ASSETS _______________

(over)

Liabilities(What you owe)

4. Short-Term Debt

i. Credit card debt _______________

ii. Short-term loans _______________

TOTAL Short-Term Debt _______________

5. Long-Term Debt

i. Mortgage ______________

ii. Other ______________

TOTAL Long-Term Debt _______________

TOTAL LIABILITIES _______________

NET WORTH

(Total Assets - Total Liabilities) _______________

DEBT-EQUITY RATIO Total Liabilities - Mortgage x 100

Net Worth _______________

Is Melody’s debt burden manageable? Explain?

________________________________________________________________

________________________________________________________________

________________________________________________________________

MAPP40S Name:______________________

Personal Finance - Review

1. Larry Fraser earns $714.85 net per week. His wife, Maureen, earns $560.25 net per week. The family receives a monthly family allowance cheque which amounts to $42.50 per child for each of their three children. Calculate the Fraser’s average monthly income.

(2)

2. The Smith’s home is valued at $155 000. Their annual insurance premium is quoted to be $0.55 per $100. How much will they need to include in their monthly budget to provide for this premium?

(2)

3. The account at which John deposits his money pays 5.25% simple interest annually. How much interest will he earn on a deposit of $7500 left in the account for 9 months?

(1)

What will be his balance in this account at the end of the year?

(2)

4. Gary has earned $65.75 in simple interest on $950 that he deposited in his account three years ago. What rate of interest was paid on this account?

(2)

5. Anne borrowed $5000 at 6.5% simple interest. How long did it take to pay the loan back if she paid $155.25 in interest (in days)?

(2)

6. Don borrowed $950 at 8.75% simple interest for 300 days. How much did he pay back at the end of that time to discharge the loan?

(2)

7. How many days will it take for a deposit of $5000 to earn $460.00 at 9% per annum simple interest?

(2)

8. A loan of $6500 is made at 6.5% for 2 years compounded monthly. Find

a) the monthly payment__________________________________________

b) The amount paid back_________________________________________

(4)

c) The interest paid_____________________________________________

N = __________________

I% = _________________

PV = _________________

PMT = _______________

FV =_________________

P/Y = ________________

C/Y =________________

PMT: ________________

9. $3000 is to be invested at 6.5% for 10 years. Using the formula, find the compound amount if interest were compounded.

a) annually

(6)

b) semi-annually

d) quarterly

10. How much must be invested at 7.5% interest compounded quarterly so that you would have $$9 000 in 10 years?

(3)

11. A $6000 loan is paid back with 25 equal payments of $285.00. What was the interest rate if the interest was compounded monthly?

a) The interest rate_____________________________________________

(4)

N = __________________

I% = _________________

PV = _________________

PMT = _______________

FV =_________________

P/Y = ________________

C/Y =________________

PMT: ________________

12. Bill wishes to have $40 000 saved for his daughters College Education. He wishes to make regular monthly deposits at the beginning of each month. He has only 10 years to save. If the investment pays 5.75% compounded monthly, how much must be deposited each month?

a) Monthly deposit

(3)

N = __________________

I% = _________________

PV = _________________

PMT = _______________

FV =_________________

P/Y = ________________

C/Y =________________

PMT: ________________

13. Bryn is 25 years old. She wishes to retire when she turns 55. She has accumulated savings of $75 000. She wishes to make additional deposits each month into her account that pays 5.5% compounded monthly. She would like to have $500 000 in her account when she retires. Find the following.

(6)

a) Her monthly deposit

b) The interest she has earned

c) If her money would earn 7.5% and she made the same deposit as in 13a), how much sooner could she retire? (Show all calculations.)

N = __________________ FV =_________________

I% = _________________ P/Y = ________________

PV = _________________ C/Y = ________________

PMT = _______________ PMT: ________________

14. Randy and Kim wish to finance a mortgage of $125 000 over 20 years. Their bank is offering mortgage loans at 7% compounded semi-annually. Find.

a) Their monthly payment

b) The total amount paid to the bank

c) The interest paid

d) If they pay the mortgage off in 15 years how much interest will they save? (show all calculations.)

(6)

N = __________________

I% = _________________

PV = _________________

PMT = _______________

FV =_________________

P/Y = ________________

C/Y =________________

PMT: ________________

15. How long would it take an investment of $7000 to earn $1659.12 interest at 6% compounded quarterly?

(1)

16. Explain the difference between simple and compound interest?

(2)

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