Chapter 1, Section 4 - Purdue University



Non Interest Theory

1. 500 + 503 + 506+509 + … + 599 =

2. If x2 + 5x +8 = 16, calculate x.

3. 1 + 3+9+27+…+59,049 =

Chapter 1, Section 4

4. A fund is earning 6% simple interest. The amount in the fund at time zero is 10,000. Calculate the amount at the end of the 5th year.

5. A fund is earning 6% simple interest. The amount in the fund at the end of the 5th year is 10,000. Calculate the amount at the end of the 10th year.

Chapter 1, Section 5

6. Nora invests 1000 at an effective annual interest rate for 10 years. After 10 years, her investment has doubled. Calculate the annual interest rate earned by Nora.

7. Chris deposits 10,000 in a bank. During the first year the bank credits an annual effective rate of interest of i. During the second year, the bank credits an annual effective rate of interest of (i-.05). At the end of two years, Chris has 12,093.75 in the bank. Calculate i.

8. Brittany invests 5000 at 5% interest compounded annually. How long will it be until Brittany has 15,000?

9. Account A pays a simple rate of interest of 20%. Account B pays a compound interest rate of 5%. What year will the annual effective interest rate for Account A be equal to the annual effective interest rate for Account B?

Chapter 1, Section 6

10. Matt wants to have 1,000,000 at age 65 when he plans to retire. Matt is now 25 and can invest money at 10% annual effective interest. Calculate the amount that Matt must invest now to achieve his goal.

11. You are given that i = 0.0915. If the present value of 1 paid in n years plus the present value of 3 paid in 2n years is 2.5431, calculate n.

12. The present value of 5 payable in 10 years plus the present value of 90 payable in 20 years is 25. Calculate i.

Chapter 1, Section 7

13. Calculate the present value of $2000 payable in 10 years using an annual effective discount rate of 8%.

14. Calculate the accumulated value at the end of 3 years of 15,000 payable now assuming an interest rate equivalent to an annual discount rate of 8%.

Chapter 1, Section 8

15. Calculate the accumulated value at the end of 3 years of 250 payable now assuming an interest rate of 12% convertible monthly.

16. Calculate the present value of $1000 payable in 10 years using a discount rate of 5% convertible quarterly.

17. A deposit is made on January 1, 2004. Calculate the monthly effective interest rate for the month of December 2004, if:

a. The investment earns an 4% compounded monthly;

b. The investment earns an annual effective rate of interest of 4%;

c. The investment earns 4% compounded semi-annually;

d. The investment earns interest at a rate equivalent to an annual rate of discount of 4%;

e. The investment earns interest at a rate equivalent to a rate of discount of 4% convertible quarterly.

f. The investment earns 4% simple interest.

18. Investment X for 100,000 is invested at a nominal rate of interest of j, convertible semi-annually. After 4 years, it accumulates to 214,358.88. Investment Y for 100,000 is invested at a nominal rate of discount of k, convertible quarterly. After two years, Investment Y accumulates to 232,305.73. Investment Z for 100,000 is invested at an annual effective rate of interest equal to j in year 1 and an annual effective rate of discount of k in year 2. Calculate the value of Investment Z at the end of two years.

19. For each of the following, given A:, calculate B:.

a. A: i=0.12 B: d(12)

b. A: i(12) = 0.12 B: i(4)

c. A: d(6) = 0.09 B: i

Chapter 1, Section 1.9

20. You are given that δ = 0.05. Calculate the accumulated value at the end of 20 years of $1000 invested at time zero.

21. You are given that δ = 0.05. Calculate the accumulated value at the end of 30 years of $1000 invested at time equal to 10 years.

22. You are given that δ = 0.05. Calculate the amount that must be invested at the end of 10 years to have an accumulated value at the end of 30 years of $1000.

Chapter 1, Section 1.10

23. You are given that δt = t/100. Calculate the accumulated value at the end of 10 years of $1000 invested at time zero.

24. You are given that δt = t/100. Calculate the accumulated value at the end of 15 years of $1000 invested at the end of the fifth year.

25. You are given that δt = t/100. Calculate the present value at the end of the 10 year of an accumulated value at the end of 15 years of $1000.

26. On July 1, 1999 a person invested 1000 in a fund for which the force of interest at time t is given by δt = .02(3 + 2t) where t is the number of years since January 1, 1999. Determine the accumulated value of the investment on January 1, 2000.

27. Calculate k if a deposit of 1 will accumulate to 2.7183 in 10 years at a force of interest given by:

a. δt = kt for 0 ................
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