Simple Interest, Compound interest, discount rate, force of interest, AV, PV

1. Fund P earns interest at a simple rate of 4% a year. Fund Q earns interest at a simple rate of i% a year. $100 is invested in fund P and $118.50 is invested in fund Q. The accumulated amount in the two funds will be equal after 5 years. Determine the simple interest rate of i.

A. .25%        B. 0.5%        C. 1%         D. 1.25%       E. 1.5%

2. Fund P earns interest at an annual effective rate of 4% a year. Fund Q earns interest at an annual effective rate of i% a year. $100 is invested in fund P and $118.50 is invested in fund Q. The accumulated amount in the two funds will be equal after 5 years. Determine the annual effective interest rate of i.

A. .25%       B. 0.5%        C. 1%       D. 1.25%      E. 1.5%

3. Sam borrows $20,000. He repays the loan 4 years later with a payment of $26,709.38. What is the annual effective interest rate on the loan?

A. 6%        B. 6.5%         C. 7%        D. 7.5%         E. 8%

4. At an annual effective interest rate of i, i > 0 all the following are equal:
i. the present value of 10,000 at the end of 6 years
ii. the sum of the present values of 6000 at the end of year t and 56,000 at the end of year 2t
iii. 5000 immediately

Calculate

A. .25         B. 0.5        C. 1          D. 1.25          E. 1.5

5. Using question 4, calculate the present value of a payment of $8000 at the end of year t+3 using the same annual effective interest rate

A. 1330      B. 1415     C. 1600     D. 1775          E. 2000

6. A deposit of $X is invested at time 6 years at an annual effective interest rate of 8%. A second deposit $X is invested at time 8 years at the same interest rate. At time 11 years, the accumulated amount of the investment is $976. Calculate X.

A. 250       B. 279        C. 300        D. 342             E. 358

7. Money accumulates in a fund at an effective annual interest rate of i during the first 5 years, and at an effective annual interest rate of 2i thereafter. A deposit of 1 is made into the fund at time 0. It accumulates to 3.09 at the end of 10 years and to 13.62 at the end of 20 years. What is the value of the deposit at the end of 7 years?

A. 1.90       B. 1.98       C. 2.06        D. 2.14          E. 2.23

8. David can receive one of the following 2 payments streams:
i. 100 at time 0, 200 at time n, 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 =0.75941, determine i.

A. 3.5%      B. 4%         C. 4.5%       D. 5%           E. 5.5%

9. A $15,000 car loan is repaid with one payment of $18,375.65 after 36 months. What is the annual effective discount rate?

A. 6.5%    B. 7%            C. 7.5%     D. 8%              E. 8.5%

10. Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 100 into his bank account, and Robbie deposits 50 into his. Each account earns an annual effective discount rate of d. The amount of interest earned in Bruce's account during the 11th year is equal to X. The amount of interest earned in Robbie's account in the 17th year is also equal to X. Calculate X.

A. 28.0      B. 31.3           C. 34.6        D. 36.7          E. 38.9

11. A deposit of $X is made into a fund which pays an annual effective interest rate of 6% for 10 years. At the same time, $X/2 is deposited into another fund which pays an annual effective rate of discount of d for 10 years. The amount of interest earned over the 10 years is equal for both funds. Calculate d.

A. 9%       B.9.5%            C. 10%         D. 10.5%        E. 11%

12. Ernie makes deposits of $100 at time 0, and $X at time 3. The fund grows at a force of interest . The amount of interest earned from time 3 to time 6 is $X. Calculate X.

A. 385        B. 485             C. 585          D. 685           E. 785

13. The force of interest

Calculate the present value of $100 payable at time 10.

A. 6.09         B. 6.20           C. 6.44          D. 6.75          E. 6.98

14. A bank agrees to lend John 10,000 now and X three years later in exchange for a single repayment of 75,000 at the end of 10 years. The bank charges an annual effective rate of 6% for the first 5 years and at a force of interest  for t > 5. Determine X.

A. 23,500     B. 24.000        C. 24,500       D. 25,000      E. 25,500

15. Which simple interest rate over six years is closest to being equivalent to the following: an effective rate of discount of 3% for the first year, an effective rate of discount of 6% for the second year, an effective rate of discount of 9% for the third year, and an effective rate of interest of 5% for the fourth, fifth and sixth years?

A. 6.3%        B. 6.4%           C. 6.5%          D. 6.6%         E. 6.7%