1 - Purdue University



Which of the following are equal to [pic].

i. v + v2 + v3

ii. [pic] - 1

iii. ([pic] )(1 – v3)

a. i and ii only

b. i and iii only

c. ii and iii only

d. All three are true

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

1. Calculate the present value of 300 paid at the end of each year for 20 years using an annual effective interest rate of 8%.

a. 2945

b. 3181

c. 3312

d. 3561

e. 3750

2. Calculate the accumulated value immediately after the last payment of a 20 year annuity due of annual payments of 500 per year. The annual effective interest rate is 7%.

a. 19,157

b. 20,498

c. 21,933

d. 23,468

e. 25,111

3. Yancy has 10,000 in a bank account earning 6% compounded monthly. Calculate the amount that he can withdraw at the end of each month from the account if he wants to have zero in the account after 12 months.

a. 857

b. 861

c. 865

d. 869

e. 873

4. For a given interest rate, [pic] = 14.2068 and [pic] = 8.3064.

Calculate n.

a. 9

b. 10

c. 11

d. 12

e. 13

5. Megan purchased a new car for 18,000. She finances the entire purchase over 60 months at a nominal rate of 12% compounded monthly.

Calculate Megan’s monthly payment.

a. 388

b. 392

c. 396

d. 400

e. 404

6. Megan wants to buy a car in 4 years for 18,000. She deposits X at the beginning of each month for four years into an account earning 6% compounded monthly.

Calculate X.

a. 327

b. 329

c. 331

d. 333

e. 335

7. Kathy wants to accumulate a sum of money at the end of 10 years to buy a house. In order to accomplish this goal, she can deposit 80 per month at the beginning of the month for the next ten years or 81 per month at the end of the month for the next ten years.

Calculate the annual effective rate of interest earned by Kathy.

a. 14.0%

b. 14.8%

c. 15.0%

d. 15.8%

e. 16.0%

8. Jeff makes payments at the end of each year into an account for 10 years. The present value of Jeff’s payments is 5,000. Ryan makes a payment equal to Jeff’s payment at the beginning of each year for 11 years into the same account. The present value of Ryan’s payments is 5,900.

Calculate the amount of Jeff’s payment.

a. 600

b. 700

c. 800

d. 900

e. 1000

9. If d = 0.05, calculate [pic].

a. 7.62

b. 7.82

c. 8.02

d. 8.73

e. 8.86

10. If d(12) = 12%, calculate the accumulated value of 100 paid at the end of each month for 12 months.

a. 1265

b. 1266

c. 1267

d. 1268

e. 1269

11. The accumulated value of an n year annuity is four times the present value of the same annuity.

Calculate the accumulated value of 100 in 2n years.

a. 100

b. 400

c. 900

d. 1600

e. 2500

12. A monthly annuity immediate pays 100 per month for 12 months. Calculate the accumulated value 12 months after the last payment using a nominal rate of 4% compounded monthly.

a. 1268

b. 1270

c. 1272

d. 1274

e. 1276

13. A monthly annuity due pays 100 per month for 12 months. Calculate the accumulated value 12 months after the last payment using a nominal rate of 4% compounded monthly.

a. 1268

b. 1270

c. 1272

d. 1274

e. 1276

14. A monthly annuity due pays 100 per month for 12 months. Calculate the accumulated value 24 months after the first payment using a nominal rate of 4% compounded monthly.

a. 1268

b. 1270

c. 1272

d. 1274

e. 1276

15. Calculate the current value at the end of 5 years of an annuity due paying annual payments of 1200 for 12 years. The annual effective interest rate is 6%.

a. 11,982

b. 12,702

c. 13,463

d. 14,271

e. 15,127

16. Calculate the present value of an annuity immediate with 20 annual payments of 500 if annuity does not start until five years have passed. The annual effective interest rate is 8%.

a. 3341

b. 3608

c. 3897

d. 4209

e. 4545

17. John buys a series of payments. The first payment of 50 is in six years. Annual payments of 50 are made thereafter until 14 total payments have been made.

Calculate the price John should pay to realize an annual effective return of 7%.

a. 291

b. 312

c. 334

d. 358

e. 382

18. Which of the following are true:

i. [pic] – [pic] = [pic]– [pic]

ii. v3 [pic] = v2 [pic]

iii. v8 [pic] = [pic] + [pic]

a. All but i.

b. All but ii.

c. All but iii.

d. All

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

19. Adam buys perpetuity immediate of 10,000 payable at the end of each year. Calculate the present value of this perpetuity using an annual effective interest rate of 5%.

a. 200,000

b. 210,000

c. 220,000

d. 230,000

e. 240,000

20. Adam buys a perpetuity due of 1000 per month for 100,000. Calculate the annual effective rate of interest used to calculate the price of this perpetuity.

a. 12.0%

b. 12.1%

c. 12.4%

d. 12.7%

e. 12.8%

21. The value of a perpetuity immediate where the payment is P is 1000 less than the value of a perpetuity due where the payment if P.

Calculate P.

a. 800

b. 900

c. 1000

d. 1100

e. 1200

22. A trust has been established such that RJ will receive a perpetuity of 1000 a year with the first payment at the end of 5 years.

Calculate the present value of the perpetuity at a discount rate of d = 8%.

a. 8009

b. 8124

c. 8239

d. 8507

e. 8955

23. A perpetuity pays 1200 at the beginning of each year with the first payment being made immediately. The trust funding the perpetuity will earn an annual effective interest rate of 10% for the first 10 years, 8% for the second 10 years and 5% thereafter.

Calculate the amount needed to fund the perpetuity immediately before the first payment.

a. 13,984

b. 15,184

c. 15,813

d. 15,964

e. 19,943

24. Julie, Chris, and Alla will share an annual perpetuity immediate of 1200. Julie will receive the first 9 payments. Chris will receive the next 16 payments. Alla will receive all remaining payments.

At an annual effective interest rate of 5%, order the value of each person’s share of the perpetuity.

a. Julie < Chris < Alla

b. Julie < Alla < Chris

c. Alla < Julie < Chris

d. Alla < Chris < Julie

e. Chris < Alla < Julie

25. Jordan inherits 50,000. This inheritance is invested in a fund earning an annual rate of interest of 6%. He withdraws 5000 per year beginning immediately. How many withdrawals of 5000 can Jordan make.

a. 10

b. 12

c. 13

d. 14

e. 15

26. Jordan inherits 50,000. This inheritance is invested in a fund earning an annual rate of interest of 6%. He withdraws 5000 per year beginning immediately. Once Jordan can no longer withdraw a full 5000, he will withdraw a final payment one year after the prior payment.

Calculate the final payment.

a. 737

b. 1,439

c. 1,665

d. 2,665

e. 3,655

27. Jenna is the beneficiary of a fund of 20,000 that pays her 1000 at the end of each month. The fund earns 6% compounded monthly. The final payment to exhaust the fund will be a balloon payment.

Calculate the amount of the balloon payment.

a. 1008

b. 1013

c. 1118

d. 1124

e. 1130

28. An annuity immediate pays 750 per year for 15 years. The accumulated value of the annuity after 15 years is 15,000.

Calculate the annual effective rate of interest used to calculate the accumulated value.

a. 3.6%

b. 3.8%

c. 4.0%

d. 4.2%

e. 4.4%

29. An annuity which pays 200 at the end of each quarter for 5 years has a present value of 3600.

Calculate the nominal rate of interest compounded quarterly.

a. 1.0%

b. 2.5%

c. 4.0%

d. 4.1%

e. 10.0%

30. An annuity due which pays 100 per month for 12 years has a present value of 7908.

Calculate the annual effective interest rate used to determine the present value.

a. 10.8%

b. 11.4%

c. 12.0%

d. 12.7%

e. 13.4%

31. A deferred perpetuity pays 500 annually beginning at the end of year 5. The present value of the deferred perpetuity is 4992.

Calculate the annual effective interest rate used to calculate the present value.

a. 5.5%

b. 6.0%

c. 6.5%

d. 7.0%

e. 7.5%

32. A fund earns 5% during the next six years and 4% during years 7 through 10. James deposits 1000 into the account now.

Calculate his accumulated value after 10 years.

a. 1564

b. 1568

c. 1572

d. 1577

e. 1582

33. A fund earns 5% during the next six years and 4% during years 7 through 10. James deposits 1000 into the account at the end of each year for the next ten years.

Calculate his accumulated value after 10 years.

a. 12,100

b. 12,204

c. 12,306

d. 12,410

e. 12,514

34. James deposits 1000 into an account at the end of each year for the next 6 years. The account earns 5% interest. James also deposits 1000 at the end of each of years 7 through 10 into another account earning 4%.

Calculate the total amount James will have in both accounts at the end of ten years.

a. 12,100

b. 12,204

c. 12,306

d. 12,410

e. 12,514

35. Which of the following is equal to the current value shown on the timeline?

[pic]

a. [pic] + [pic]

b. [pic] + [pic]

c. [pic] (1+i)3

d. v4 [pic]

e. [pic] + (1+i) [pic]

36. If [pic] times [pic] = 4.05, calculate i.

a. 5%

b. 10%

c. 15%

d. 20%

e. 25%

37. Which of the following are true:

i. [pic] + 1 = [pic]

ii. [pic] – [pic] = v2 [pic]

iii. ([pic])(1+i) -1 = [pic]

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.

38. A perpetuity pays 1 at the beginning of every year. The present value is 10.

Calculate the annual effective rate of interest earned by the perpetuity.

a. 8.9%

b. 9.5%

c. 10.0%

d. 10.5%

e. 11.1%

39. [pic] = X. [pic] = 1.25X.

Calculate the interest rate used.

a. 5%

b. 10%

c. 15%

d. 20%

e. 25%

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