Stat 274 Practice Exam 1 - Page 1 of 4

Stat 274

Practice Exam 1 - Page 1 of 6

There are 33 questions on this exam, each worth the same number of points. There is no partial credit for leaving an answer blank. Unless specified, assume that the time is in years.

1. Anne pays Brandon 200 at time 0, Brandon pays Anne 80 at times 1, 2, 3, and 10. Each time Anne receives a payment, she invests it in a separate account earning 5% effective interest and then withdraws all the money at time 10. Calculate the difference between Anne's yield rate and the interest rate Brandon pays (subtract the smaller value from the larger value).

A. Less than 7.5% B. At least 7.5%, but less than 8.0% C. At least 8.0%, but less than 8.5% D. At least 8.5%, but less than 9.0% E. At least 9.0%

2. What is the present value of an annuityimmediate which pays 10 per year for the first 20 years and 30 per year for the next 20 years at an annual effective interest rate of 5%?

A. Less than 260 B. At least 260, but less than 270 C. At least 270, but less than 280 D. At least 280, but less than 290 E. At least 290

3. Jim deposits 100 into a bank account paying a nominal interest rate of 6% convertible quarterly. At the same time, Gail deposits 50 into an account paying a force of interest of . After 15.25 years, the accounts have the same balance. Calculate .

A. Less than 0.06 B. At least 0.06, but less than 0.08 C. At least 0.08, but less than 0.10 D. At least 0.10, but less than 0.12 E. At least 0.12

4. You deposit 125 into an account which pays an annual effective discount rate of d. If the balance of the account is less than 150, d = 4%. If the account balance is between

150 and 200, the effective rate of discount is d = 5%. If the account balance is greater than 200, the effective rate of discount is d = 6%. How many years does it take for the account balance to grow to 225?

A. Less than 10 B. At least 10, but less than 11 C. At least 11, but less than 12 D. At least 12, but less than 13 E. At least 13

5. You buy an annuity which pays 100 at time 1, 100(1 + g) at time 2, 100(1 + g)k-1 at time k, through 100(1 + g)49 at time 50. You could have instead purchased a perpetuity paying 110 at the end of each year for the same price. If i = 0.04, calculate g.

A. Less than 0.01 B. At least 0.01, but less than 0.02 C. At least 0.02, but less than 0.03 D. At least 0.03, but less than 0.04 E. At least 0.04

6. If t = 0.01 + 0.001t + 0.0001t3, how much will 100 at time 2 grow to become at time 7?

A. Less than 100 B. At least 100, but less than 110 C. At least 110, but less than 120 D. At least 120, but less than 130 E. At least 130

7. You put 20 into a savings account at the end of every other month (if t is in months, at times 1, 3, 5, . . .). Assuming the annual effective interest rate is 2%, how many months will it take for you to accumulate 3000 in your account?

A. Less than 100 B. At least 100, but less than 110 C. At least 110, but less than 120 D. At least 120, but less than 130

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E. At least 130

B. At least 0.5%, but less than 2.5%

8. You buy a perpetuity paying 20 per year, at the end of each year. Immediately after the 7th payment, you sell the remaining payments in your perpetuity and buy a 10-year annuity immediate. Assuming the annual effective interest rate is 6%, how large will each of your 10 annuity payments be?

A. Less than 40

B. At least 40, but less than 44

C. At least 44, but less than 48

D. At least 48, but less than 52

E. At least 52

9. At time 0, you buy an annuity which pays 10 at times 1, 2, 3, . . ., 29, and 30. You do not have to pay for this annuity until time 45. Assuming the annual effective interest rate is 4%, what will you need to pay for the annuity (at time 45)?

A. Less than 400

C. At least 2.5%, but less than 4.5%

D. At least 4.5%, but less than 6.5%

E. At least 6.5%

12. Alice has a very flexible banker who allows her to deposit 2000 into account A with an annual effective interest rate of 7%. In five years she takes half of the interest earned in that account and deposits it into a new account B earning 2% convertible quarterly. At time 16 she takes all the interest earned in account A between times 10 and 16 and transfers it to account B. Now, at year 20, what is the absolute difference between accounts A and B?

A. Less than 1250

B. At least 1250, but less than 1500

C. At least 1500, but less than 1750

D. At least 1750, but less than 2000

E. At least 2000

B. At least 400, but less than 600 C. At least 600, but less than 800 D. At least 800, but less than 1000 E. At least 1000

10. You borrow some money and can either repay it by making (a) two payments of 20 at times 5 and 15 or (b) a single payment of 45 at time 15. Calculate the annual effective interest rate.

A. Less than 1.5% B. At least 1.5%, but less than 2.0% C. At least 2.0%, but less than 2.5% D. At least 2.5%, but less than 3.0% E. At least 3.0%

11. To be fair to your two children, you give them a gift. One gets two payments of 100, at times 0 and 1. The other receives a perpetuity paying 1 at times 1, 2, 3, . . .. Calculate the annual effective interest rate.

13. Always the worrier, you want to make sure you have enough money for your wife's birthday presents every year. You want to have 100 each year forever in an account that earns 8% interest. You and your future wife both turned 15 today, assume you will need the money starting on her 23rd birthday. How much do you need to invest today in order to have the necessary amount on her 23rd birthday?

A. Less than 700

B. At least 700, but less than 800

C. At least 800, but less than 900

D. At least 900, but less than 1000

E. At least 1000

14. A perpetuity-immediate pays X per year. Ernie receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Ernie's share of the present value of the original perpetuity is 40%. Calculate Jeff's share.

A. Less than 0.5%

A. Less than 26%

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B. At least 26%, but less than 30%

C. At least 30%, but less than 34%

D. At least 34%, but less than 38%

E. At least 38%

15. You can buy a deferred annuity for 21,092.04. The annuity pays twelve annual payments of X, the first of which is 12 years from today. The annuity yields 7.8%. Calculate X.

A. Less than 6,250

B. At least 6,250, but less than 6,300

C. At least 6,300, but less than 6,350

D. At least 6,350, but less than 6,400

E. At least 6,400

16. You purchase a perpetuity-immediate. It pays 1,000 at the end of each of the first 11 years and then the payments increase by 180 each year. To be clear, the payment at time 11 is 1,000, and at time 12 the payment is 1,180. Calculate the purchase price assuming a 5% annual effective interest rate.

A. Less than 63,000

B. At least 63,000, but less than 64,000

C. At least 64,000, but less than 65,000

D. At least 65,000, but less than 66,000

E. At least 66,000

17. To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years. The annual effective rate of interest is i. You are given (1 + i)n = 2.0. Determine i.

A. Less than 11.5%

B. At least 11.5%, but less than 12.0%

C. At least 12.0%, but less than 12.5%

D. At least 12.5%, but less than 13.0%

E. At least 13.0%

18. You can receive one of the following two payment streams:

(i) 100 at time 0, 200 at time n, and 300 at time 2n

(ii) 600 at time 10

At an annual effective interest rate of i, the present values of the two streams are equal. Given vn = 0.76, determine i.

A. Less than 3.75% B. At least 3.75%, but less than

4.25% C. At least 4.25%, but less than

4.75% D. At least 4.75%, but less than

5.25% E. At least 5.25%

19. You invest X into an account earning an annual effective interest rate of i. The interest earned in the 2nd year is X/2. Calculate i.

A. Less than 1% B. At least 1%, but less than 3% C. At least 3%, but less than 5% D. At least 5%, but less than 7% E. At least 7%

20. You borrow 3000 at an annual effective rate of 8% and pay it back with one payment of 1000 at the end of the first year, 500 at the end of the second, and another payment of X at the end of the third. Calculate X.

A. Less than 2000 B. At least 2000, but less than 2050 C. At least 2050, but less than 2100 D. At least 2100, but less than 2150 E. At least 2150

21. You pay off a loan with monthly payments of 90 for 10 years. The annual effective interest rate is 5%. What is the outstanding loan balance immediately after the 15th payment?

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A. Less than 7000 B. At least 7000, but less than 7500 C. At least 7500, but less than 8000 D. At least 8000, but less than 8500 E. At least 8500

22. You take out a loan of 5000 at a nominal rate of 5.4% convertible monthly. Your first 59 monthly payments are 96, and the last payment is smaller. You miss the 3rd and 17th payments. What is the outstanding loan balance immediately after the 12th payment? A. Less than 3400 B. At least 3400, but less than 3700 C. At least 3700, but less than 4000 D. At least 4000, but less than 4300 E. At least 4300

23. You borrow 200 at an annual effective rate of 3%. After 3 end-of-year payments of 20, how much interest have you paid? (Note that there are still many payments to be made) A. Less than 15.50

8 years, you sell the home for 282000. Closing costs are 3% of the sale price. How much did you receive at closing?

A. Less than 60000 B. At least 60000, but less than 80000 C. At least 80000, but less than

100000 D. At least 100000, but less than

120000 E. At least 120000

26. You purchase a home for 300,000, make a down payment of 140,000, then finance the rest with a thirty year mortgage at an annual effective interest rate of 6.5%. After exactly 8 years, you sell the home for 282000. Closing costs are 3% of the sale price. How much did you pay in interest over the 8 years?

A. Less than 50000 B. At least 50000, but less than 60000 C. At least 60000, but less than 70000 D. At least 70000, but less than 80000 E. At least 80000

B. At least 15.50, but less than 16.50 C. At least 16.50, but less than 17.50 D. At least 17.50, but less than 18.50 E. At least 18.50

24. You take out a loan of 100,000 and will repay it with 35 monthly payments of Q and a last (36th) monthly payment of R. Assuming the annual effective interest rate is 4.5%, calculate the difference, Q - R (Note that each payment must be in whole cents). A. Less than 0.00 B. At least 0.00, but less than 0.04 C. At least 0.04, but less than 0.08 D. At least 0.08, but less than 0.12

27. You take out a loan which will be repaid with 10 annual payments at an annual effective interest rate of 6%. The first payment will be at time 1. The first four payments are 850 each and the last six are 1250 each. What is the outstanding loan balance immediately after the 6th payment?

A. Less than 4,230 B. At least 4,230, but less than 4,330 C. At least 4,330, but less than 4,430 D. At least 4,430, but less than 4,530 E. At least 4,530

28. A 10-year loan of 2,000 is to be repaid with payments at the end of each year. It can be repaid under the following two options:

E. At least 0.12

25. You purchase a home for 356,000, make a down payment of 140,000, then finance the rest with a thirty year mortgage at an annual effective interest rate of 6.5%. After exactly

(i) Equal annual payments at an annual effective rate of 8.07%.

(ii) Installments of 200 each year plus interest on the unpaid balance at an annual effective rate of i.

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The sum of the payments under option (i) equals the sum of the payments under option (ii). Determine i.

A. Less than 8.8% B. At least 8.8%, but less than 9.1% C. At least 9.1%, but less than 9.4% D. At least 9.4%, but less than 9.7% E. At least 9.7%

29. You borrow X for four years at an annual effective interest rate of 8%, to be repaid with equal payments at the end of each year. The outstanding loan balance at the end of the third year is 559.12. Calculate the principal repaid in the first payment.

A. Less than 445 B. At least 445, but less than 455 C. At least 455, but less than 465 D. At least 465, but less than 475 E. At least 475

D. At least 44%, but less than 46% E. At least 46%

32. A loan of L at a nominal rate of 3% convertible monthly is repaid with 180 monthly payments of X. The ratio, L/X = 144.8 and the amount of interest in the first mortgage payment is 626.42. Calculate X.

A. Less than 1,750 B. At least 1,750, but less than 1,800 C. At least 1,800, but less than 1,850 D. At least 1,850, but less than 1,900 E. At least 1,900

33. A loan is to be repaid by monthly payments of 800 for 36 months, each paid at the end of the month. The interest contained in the 27th payment is 15.78 more than the interest in the 32nd payment. Find the effective monthly rate of interest. (Note that the interest rate is less than 100%)

A. Less than 0.5%

30. You take out a 10,000 loan repaid with annual payments for twelve years. The annual effective interest rate is 2% for the first two years and 6% for the remainder. What is the loan balance immediately after the fifth payment?

B. At least 0.5%, but less than 1.5% C. At least 1.5%, but less than 2.5% D. At least 2.5%, but less than 3.5% E. At least 3.5%

A. Less than 5,000

B. At least 5,000, but less than 5,500

C. At least 5,500, but less than 6,000

D. At least 6,000, but less than 6,500

E. At least 6,500

31. Kate purchased a Ferrari for 180,800. She paid a down payment of 38,000 and the rest is paid with a 20 end-of-the-month payments with a nominal interest rate of 3.36% convertible monthly. What portion of the loan's total interest is incurred between the 7th and 18th payments?

A. Less than 40%

B. At least 40%, but less than 42%

C. At least 42%, but less than 44%

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