1 - Purdue University



An annuity pays 100 at the end of each quarter for 10 years.

Calculate the present value of the annuity using an annual effective interest rate of 12%.

a. 2300

b. 2306

c. 2311

d. 2340

e. 2359

1. An annuity pays 100 at the end of each quarter for 10 years.

Calculate the present value of the annuity using a nominal interest rate of 12% compounded monthly.

a. 2300

b. 2306

c. 2311

d. 2340

e. 2359

2. An annuity pays 100 at the end of each quarter for 10 years.

Calculate the present value of the annuity using a nominal interest rate of 12% compounded six times per year.

a. 2300

b. 2306

c. 2344

d. 2340

e. 2359

3. An annuity pays 1000 at time 0, time 3, time 6, etc until 20 payments have been made.

Calculate the accumulated value at the end of 60 years using an annual effective interest rate of 6%.

a. 146,628

b. 167,461

c. 173,021

d. 186,431

e. 199,448

4. An annuity pays 1000 at time 0, time 3, time 6, etc until 20 payments have been made.

Calculate the accumulated value immediately after the last payment using an annual effective interest rate of 6%.

a. 146,628

b. 167,461

c. 173,021

d. 186,431

e. 199,448

5. An annuity pays 500 at the start of each year for 15 years.

Calculate the accumulated value of the annuity after 15 years assuming a constant force of interest of 5%.

a. 10,789

b. 10,893

c. 11,328

d. 11,452

e. 11,894

6. A perpetuity pays 100 at the end of every third year. The first payment is in three years.

Calculate the present value of the perpetuity using a constant force of interest of 10%.

a. 286

b. 302

c. 318

d. 951

e. 1000

7. An annuity pays 100 at the end of each month forever.

Calculate the present value of the annuity using an annual effective interest rate of 8%.

a. 10,000

b. 12,500

c. 13,750

d. 15,000

e. 15,542

8. An annuity pays 100 at the end of each month forever. Using an annual effective interest rate of 8%, calculate the present value of future payments immediately after the 12th payment.

a. 10,000

b. 12,500

c. 13,750

d. 15,000

e. 15,542

9. An annuity pays 100 at the end of each month for 20 years. Using a nominal rate of interest of 4% compounded quarterly, calculate the current value of the annuity at the end of the 3rd year.

a. 16,521

b. 17,890

c. 18,069

d. 18,584

e. 18,617

10. Which of the following are true:

i. [pic]= (i(m)/i) [pic]

ii. [pic] = (1+i)n [pic]

iii. [pic] = [pic]

a. All but i

b. All but ii

c. All but iii

d. All statements are true

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

11. If δ = 0.06, calculate [pic].

a. 12.6

b. 12.9

c. 13.2

d. 13.4

e. 13.7

12. If δ = .01t, calculate [pic].

a. 3.03

b. 3.07

c. 3.11

d. 3.15

e. 3.20

13. If [pic] = 4 [pic]. Calculate δ.

a. 5.05

b. 5.20

c. 5.33

d. 5.49

e. 5.65

14. You are given that [pic] = (1.05)2t.

Calculate δ.

a. 2.47%

b. 5.00%

c. 5.25%

d. 10.00%

e. 10.25%

15. An annuity pays 10 at the end of the first year, 20 at the end of the second year, 30 at the end of the third year, etc. The last payment is made at the end of the 12th year.

Calculate the accumulated value of this annuity immediately after the last payment using an annual effective rate of 4%.

a. 756.45

b. 786.70

c. 871.84

d. 906.71

e. 942.98

16. A 20 year annuity immediate pays 500 + 50t at the end of year t.

Calculate the present value of this annuity using an annual effective rate of 6%.

a. 10,096

b. 10,304

c. 10,670

d. 11,243

e. 11,622

17. A 10 year annuity due pays 1000 as the first payment. Each subsequent payment is 50 less than the prior payment.

Calculate the current value of the annuity at the end of 5 years using an annual effective rate of 8%.

a. 5410

b. 7360

c. 7951

d. 7962

e. 8586

18. Which of the following are true:

i. [pic] + [pic] = (n) ([pic])

ii. [pic]

iii. [pic]

a. All but i

b. All but ii

c. All but iii

d. All statements are true

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

19. A perpetuity pays 200 at the end of each of the first two years, 300 at the end of years 3 and 4, 400 at the end of years 5 and 6, etc.

Calculate the present value of this perpetuity if the annual effective rate of interest is 10%.

a. 4762

b. 5762

c. 6762

d. 7762

e. 8762

20. A 20 year increasing annuity due pays 100.00 at the start of year 1, 105.00 at the start of year 2, 110.25 at the start of year 3, etc. In other words, each payment is 5% greater than the prior payment.

Calculate the present value of this annuity at an annual effective rate of 5%

a. 1645

b. 1728

c. 1814

d. 1905

e. 2000

21. A 10 year increasing annuity due pays 1 at the start of year 1, 1.1025 at the start of year 2, 1.2155063 at the start of year 3, etc. In other words, each payment is 10.25% greater than the prior payment. Which of the following symbolically are equal to the present value of this annuity using an interest rate of 5%?

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

22. A perpetuity pays 1000 at the beginning of the first year. Each subsequent payment is increased by inflation. If inflation is assumed to be 4% per year, calculate the present value of this perpetuity using an annual effective interest rate of 10%.

a. 16,667

b. 17,333

c. 17,667

d. 18,333

e. 18,667

23. A perpetuity pays 1000 at the beginning of the first year. Each subsequent payment is increased by inflation. If inflation is assumed to be 4% per year, calculate the present value of this perpetuity using an annual effective interest rate of 4%

.

a. 25,000

b. 50,000

c. 100,000

d. 200,000

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

24. A 50 year annuity pays 1 at the end of year 1 and increases by 1 each year until the payment is 20 at the end of year 20. The payment then remains level at 20 through the end of year 31. Payments then decrease by 1 each year until a payment of 1 is paid at the end of year 50. Calculate the accumulated value of this annuity immediately after the last payment using an annual effective interest rate of 3%

a. 306

b. 524

c. 812

d. 1344

e. 1616

25. P1 is the sum of the payments made by the annuity whose symbol is [pic].

P2 is the sum of the payments made by the annuity whose symbol is [pic].

Calculate P1 – P2.

a. -12.50

b. -1.25

c. 0

d. 1.25

e. 12.50

26. A 20 year annuity pays 10 at the beginning of each quarter during the first year, 20 at the beginning of each quarter during the second year, etc with 200 being paid at the beginning of each quarter during the last year.

Calculate the present value of the annuity assuming an annual effective interest rate of 12%.

a. 1850

b. 1878

c. 1932

d. 2190

e. 2253

27. A 20 year annuity pays 10 at the beginning of each quarter during the first year, 20 at the beginning of each quarter during the second year, etc with 200 being paid at the beginning of each quarter during the last year.

Calculate the accumulated value of the annuity assuming a nominal interest rate of 6% compounded monthly.

a. 11,579

b. 11,754

c. 12,917

d. 13,112

e. 13,309

28. A perpetuity paid continuously at a rate of 100 per year has a present value of 800.

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

.

a. 11.8%

b. 12.1%

c. 12.5%

d. 12.9%

e. 13.3%

29. A 20 year annuity pays 10 at the end of the first quarter, 20 at the end of the second quarter, etc with each payment increasing by 10 until the last quarterly payment is made at the end of the 20th year.

Calculate the present value of the annuity assuming an annual effective interest rate of 12%.

a. 7968

b. 8049

c. 8280

d. 8518

e. 8763

30. A 20 year annuity pays 10 at the end of the first quarter, 20 at the end of the second quarter, etc with each payment increasing by 10 until the last quarterly payment is made at the end of the 20th year.

Calculate the present value of the annuity assuming a nominal interest rate of 6% compounded monthly.

a. 3,785

b. 15,141

c. 15,487

d. 60,564

e. 242,256

31. A perpetuity pays 1000 immediately. The second payment is 97% of the first payment and is made at the end of the fourth year. Each subsequent payment is 97% of the previous payment and is paid four years after the previous payment.

Calculate the present value of this annuity at an annual effective rate of 8%.

a. 2484

b. 2561

c. 3484

d. 3561

e. 9818

32. If δ = 0.06, calculate the present value of a continuous annuity of 1 payable for 20 years.

a. 11.47

b. 11.65

c. 11.81

d. 12.16

e. 12.50

33. If i = 0.04, calculate the accumulated value of a continuous annuity payable at a rate of 100 per year for 10 years.

a. 1176

b. 1201

c. 1224

d. 1230

e. 1249

34. Lauren is being paid a continuous perpetuity payable at a rate of 1000 per year. Calculate the present value of the perpetuity assuming d(12) = 0.12.

a. 7802

b. 7812

c. 8298

d. 8250

e. 8292

35. If δ = 0.06, calculate the present value of 10 year continuous annuity payable at a rate of s at time s.

a. 29.60

b. 30.91

c. 32.50

d. 33.86

e. 34.02

36. A 10 year continuous annuity pays at a rate of t at time t. If vt = .94t, calculate the accumulated value of the annuity after ten years.

a. 33.46

b. 35.31

c. 38.39

d. 62.13

e. 71.28

37. A 30 year continuous annuity pays at a rate of t at time t. If δ = 0.10, calculate the current value of the annuity after ten years.

a. 80

b. 218

c. 310

d. 592

e. 1609

38. A 10 year continuous annuity pays at a rate of t2 + 2t + 1 at time t. Calculate the present value of this annuity if δt = (1+t)-1.

a. 60

b. 110

c. 210

d. 310

e. 443

39. Janice is receiving a perpetuity of 100 at the end of each year. Megan is receiving a perpetuity that pays 10 at the end of the first year, 20 at the end of the second year, 30 at the end of the third year, etc. The present values of the two perpetuities are equal. Calculate the annual effective interest rate used to determine the present values.

a. 1/8

b. 1/9

c. 1/10

d. 1/11

e. 1/12

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