1. What is the Macaulay duration of a level perpetuity with an annual interest rate of 3.42%. Assume annual end of year payments. [30.2398]

A. Less than 25

B. At least 25, but less than 30

C. At least 30, but less than 35

D. At least 35, but less than 40

E. At least 40

2. The bank loans out 3000 each to 1500 individuals. They want to make back an average of 3600 on these loans but they expect that a certain number of these individuals will default. You are given the following:

• 16 are expected to default with 45% recovery

• 11 are expected to default with 23% recovery

• 2 are expected to default with no recovery

What is the adjusted amount the bank should require to account for these defaults? [3646.85]

A. Less than 3620

B. At least 3620, but less than 3630

C. At least 3630, but less than 3640

D. At least 3640, but less than 3650

E. At least 3650

3. For an n-year bond the ratio of the per-period effective interest rate to the modified coupon rate is 6/11. The present value of the redemption value is 3000. v

n = 0.766416732. What is the price of the bond? [4676.25]

A. Less than 4675

B. At least 4675, but less than 4677

C. At least 4677, but less than 4679

D. At least 4679, but less than 4681

E. At least 4681

4. You invest 200 at time 0 into an account which pays a force of interest of t 2/100. At what time will the account balance grow to 350? [5.52]

A. Less than 5

B. At least 5, but less than 5.2

C. At least 5.2, but less than 5.4

D. At least 5.4, but less than 5.6

E. At least 5.6

5. A perpetuity pays 10 at time 1, (10 · 1.02) + 5 at time 2, (10 · 1.022) + 2 · 5 at time 3, continuing in that pattern where the time t payment is 10(1.02t−1) + 5(t − 1). Using i = 0.03, find the present value of this perpetuity. [6555.56]

A. Less than 6750

B. At least 6750, but less than 7000

C. At least 7000, but less than 7250

D. At least 7250, but less than 7500

E. At least 7500

6. You give your children a perpetuity which pays X at the beginning of every year. Abby takes the first 15 payments and Sophie gets the rest. The present value of each child’s share is equal. What is the annual effective interest rate? [0.0473]

A. Less than 0.02

B. At least 0.02, but less than 0.03

C. At least 0.03, but less than 0.04

D. At least 0.04, but less than 0.05

E. At least 0.05

7. You buy a unique annuity which pays 1 and the end of each month for the first 12 months, 2 at the end of each month for the next 12, 3 for the next 12, increasing arithmetically until it pays 70 at the end of each month for months 829-840.

Assuming a nominal interest rate of 0.12 convertible monthly, calculate the present value of this annuity. [886.64]

A. Less than 875

B. At least 875, but less than 880

C. At least 880, but less than 885

D. At least 885, but less than 890

E. At least 890

8. You take out a loan and will repay it with 17 annual payments of X. Immediately before the 7th payment, the loan balance is p · X. The annual effective interest rate is 0.06. Calculate p. [8.36]

A. Less than 8.2

B. At least 8.2, but less than 8.3

C. At least 8.3, but less than 8.4

D. At least 8.4, but less than 8.5

E. At least 8.5

9. You borrow 10,000 and repay it with 48 monthly payments of 250. You miss the 12th and 19th payments. Calculate the outstanding loan balance immediately after the 15th payment. [7516.38]

A. Less than 7480

B. At least 7480, but less than 7500

C. At least 7500, but less than 7520

D. At least 7520, but less than 7540

E. At least 7540

10. Find the Macaulay duration of a 15-year mortgage for X at an annual effective interest rate of 0.06. [6.463]

A. Less than 6.1

B. At least 6.1, but less than 6.3

C. At least 6.3, but less than 6.5

D. At least 6.5, but less than 6.7

E. At least 6.7