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

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.

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?

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%.

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:.

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

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

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

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.

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:

j. δt = kt for 0 ................
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