1 - Purdue University



A fund is earning 5% simple interest.

Calculate the effective interest rate in the 6th year.

a. 2.5%

b. 3.0%

c. 4.0%

d. 5.0%

e. 6.0%

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

Calculate the amount in the fund at the end of 7 year.

a. 10,800

b. 10,900

c. 11,000

d. 11,100

e. 11,200

2. Calculate the present value of a payment of 10,000 to be made in 17 years assuming a simple rate of discount of 3%.

a. 4,900

b. 5,100

c. 5,958

d. 6,050

e. 6,623

3. Fund A earns interest at a nominal rate of interest of 12% compounded quarterly. Fund B earns interest at a force of interest δ. John invested $1,000 in each fund five years ago. Today, the amount in Fund A is equal to the amount in Fund B.

Calculate δ.

a. 11.7%

b. 11.8%

c. 11.9%

d. 12.0%

e. 12.1%

4. Fund A earns interest at a nominal rate of interest of 12% compounded quarterly. Fund B earns interest at a force of interest δ. John invested $1,000 in each fund five years ago. Today, the amount in Fund A is 150% of the amount in Fund B.

Calculate δ.

a. 3.7%

b. 6.0%

c. 6.2%

d. 6.6%

e. 6.8%

5. Fund A earns interest at a nominal rate of 6% compounded monthly. Fund B earns interest at a nominal rate of discount of compounded three times per year. The annual effective rate of interest earned by both funds is equal.

Calculate the nominal rate of discount earned by Fund B.

a. 1.49%

b. 1.98%

c. 5.93%

d. 5.94%

e. 5.95%

6. A fund earns interest at a constant force of interest of δ = 0.05.

Calculate the value at the end of five years of 8,000 invested today.

a. 10,210

b. 10,241

c. 10,272

d. 10,500

e. 10,799

7. A fund earns interest at a force of interest of δ = 0.01t.

Calculate the value at the end of five years of 8,000 invested today.

a. 8,410

b. 9,065

c. 9,270

d. 9,666

e. 10,272

8. A fund earns interest at a force of interest of δ = 0.01t.

Calculate the value at the end of 10 years of 8,000 invested at the end of 5 years.

a. 9,065

b. 9,270

c. 10,272

d. 10,820

e. 11,640

9. Which of the following are true:

i. i – d = id

ii. iv = d

iii. d = 1 – v

a. i only

b. ii only

c. iii only

d. i and iii only

e. The correct answer is not given by a., b., c., or d.

10. A fund earns interest at a force of interest of δ = 0.01t.

Calculate the effective rate of interest in 10th year.

a. 9.0%

b. 9.5%

c. 10.0%

d. 10.5%

e. 11.0%

11. A fund will earn a nominal rate of interest of 5% compounded quarterly during the first two years, a nominal rate of discount of 4% compounded monthly during years 3 and 4, and a constant force of interest of 3% during the fifth and sixth year.

Calculate the amount that must be invested today in order to accumulate 5,000 after 6 years.

a. 3935

b. 3936

c. 3944

d. 3951

e. 3952

12. SA(t) is the amount function under simple interest. CA(t) is the amount function under compound interest. Which of the following are true:

i. SA(t) is equal to CA(t) only at t = 1

ii. SA(t) is less than CA(t) for all t > 1

iii. SA(t) is greater than CA(t) for 0 < t < 1

a. i only

b. ii only

c. iii only

d. i and ii only

e. The correct answer is not given by a., b., c., or d.

13. Which of the following are true for a(t):

i. a(0) = 1

ii. a(t) is an increasing function

iii. a(t) is a continuous function

a. i only

b. ii only

c. iii only

d. i and ii only

e. The correct answer is not given by a., b., c., or d.

14. Which of the following are true:

i. i = a(1) – 1

ii. A(k)/a(k) = k

iii. The effective interest rate under simple interest, in, is a decreasing function of n.

a. All but i.

b. All but ii.

c. All but iii

d. All are true

e. The correct answer is not given by a., b., c., or d.

15. Calculate the effective annual interest rate equivalent to a nominal rate of interest of 6% compounded continuously.

a. 6.00%

b. 6.17%

c. 6.18%

d. 6.19%

e. 6.20%

16. Calculate the effective annual interest rate equivalent to a nominal rate of discount of 6% compound continuously.

a. 6.00%

b. 6.17%

c. 6.18%

d. 6.19%

e. 6.20%

17. If i(8) = 0.16, calculate d(½).

a. 13.6%

b. 14.6%

c. 16.6%

d. 17.6%

e. 18.6%

18. If a(t) = 1 + .01(t2+t), calculate δ5.

a. 8.00%

b. 8.11%

c. 8.24%

d. 8.33%

e. 8.46%

19. You are given that v = 0.80. Calculate d.

a. 1/3

b. 1/4

c. 1/5

d. 1/6

e. 1/7

20. A fund earns a nominal rate of 8% compounded quarterly.

Calculate the accumulated value of 1000 after 6.75 years.

a. 1577

b. 1673

c. 1681

d. 1707

e. 1741

21. A fund earns a nominal rate of interest of 6% compounded every two years.

Calculate the amount that must be contributed now to have 1000 at the end of six years.

a. 507

b. 606

c. 705

d. 712

e. 840

22. A fund earns a nominal rate of interest of 6% compounded every two years.

Calculate the amount that must be contributed now to have 1000 at the end of one year.

a. 890

b. 893

c. 941

d. 943

e. 945

23. 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.

a. 1036

b. 1046

c. 1064

d. 1083

e. 1094

24. 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.

a. 223

b. 231

c. 368

d. 377

e. 607

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.

a. 515

b. 525

c. 535

d. 545

e. 555

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

i. δt = kt for 0 ................
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