Installment Loans (amortized loans) Installment Loan ...

Checklist and Assignment

Checklist: Installment Loan Basics Credit Cards Mortgages

Assignment: 1. p 261 - 262 Quick Quiz 2. p 263 Exercises 13, 15, 17, 20, 22, 27, 30, 37 Keep up practice by using your calculator!

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Notes

Key Words

Installment Loans (amortized loans) Installment Loan Formula Mortgages Installment Loan Formula

PMT =

P?

APR n

1-

1

+

APR n

(-nY )

Notes

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Loans

In this unit we use the math involved with loans, credit cards, and mortgages.

We will:

Find the right amount for a monthly payment to pay back a loan during Y years.

Compare the payment towards a principal and towards interest each payment.

Compare the lifetime amount of payments of a loan and the total interest.

Compare monthly payments and total loan costs for different options.

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Notes

Example

Suppose you borrow $7000 for tuition at an annual interest rate of APR = 6%, or 0.5% per month. At the end of the first month, you owe interest in the amount of

0.5% ? $7000 = $35

Only paying $35 will pay off the interest.

By paying $235, the interest will be paid and a loan principal of $6800 remains. The next interest amount is

0.5% ? $6800 = $34

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Notes

Example

Suppose the same loan ($7000 and APR = 6%) is taken and you want to pay it off in 3 years. The exact payments can be calculated with

PMT =

P?

APR n

1-

1

+

APR n

(-nY )

PMT

=

[1

$7000

?

0.06 12

-

(1

+

0.06 12

)(-12?3)]

=

$212.95

Monthly payments of $212.95 each month will repay the

loan after 3 years.

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Notes

Using the Formula

Suppose your student loans total $7500 upon graduation. The interest rate is APR = 9% and the loan term is 10 years. What are:

your monthly loan payments? your total payments over 10 years? the total interest paid on the loan?

Ans: $95.01 per month, $11,401.20, $3,901.20.

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Principal and Interest Payments

What portion of the $95.01 goes towards interest and goes towards principal during the first three months? For each month, 9%/12 = 0.75%.

Month Interest Payment toward Principal

Ans:

1 2

$56.25 $55.96

$38.76 $39.05

3 $55.67

$39.34

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Notes

Choice of Loans

Notes

When seeking a loan, usually you have choices of interest rates and loan terms. Which has higher monthly payments: short-terms / long-terms, low interest / high interest?

Example You need a loan of $8,000. A bank offers a 3-year loan at 8%, a 4-year loan at 9%, and a 5-year loan at 10%. Calculate monthly payments and total interest over time with each option.

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Credit Cards

Credit card loans differ by not requiring the loan to be paid off in any set period of time. Most credit cards have high interest rates and low minumum payments. Often the minimum payment is lower than the amount of interest gained on the principal.

Suppose a credit card has a balance of $2300, with an annual interest rate of 21%. You decide to pay off the balance after 1 year, assuming you make no other credit card purchases. How much should you pay each month?

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Notes

Mortgages

A popular type of installment loan is a home mortgage. Interest rates tend to be lower. These loans usually involve a down payment and an additional fee called a 'closing cost.' The simplest type of a loan is a fixed rate mortgage with terms of 15 or 30 years.

The loan payment formula is used to calculate payments for fixed rate mortgages.

Closing costs are fees charged as points, using 1 point = 1% of the loan.

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Notes

Mortgages

Notes

A loan of $100,000 is needed for a new home. The bank offers a choice of a 30-year loan at an APR of 8% or a 15-year loan at 7.5%. Compare the monthly payments and total loan costs of each options. Assume the closing costs are the same and do not affect the choice.

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Practical Matters

Notes

How do the proportions of payments toward interest and principal change over time?

What are drawbacks to short/long loans? Low/high interest rates?

What might be reasons of offering low/high interest rates?

Tips on avoiding credit card trouble, refinancing loans are on pagese 255, 257.

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