1. TM 661 Problems, Problems, Problems

2. Changing Interest Stu deposits $5,000 in an account that pays interest at a rate of 9% compounded monthly. Two years after the deposit, the account begins paying interest at a rate of 6% compounded monthly. How much is the account balance five years after the deposit?

3. Changing Interest 5,000 24 60 3/4% 1/2% F F’ = P’ F F P ',,,  5000 3 4 24 ( )

4. Changing Interest 5,000 24 60 3/4% 1/2% F F’ = P’ F F P ',,,  5000 3 4 24 FP F P  ',,,(. ) (. ) 1 2 36500010075 1 005 24 36 = $7,159 ( )

5. Beginning of Period Adj. Carol deposits $200 into a savings account on January 1. On the first of each month she continues to make regular deposits of $200 into the account, making her last deposit December 1. Assuming the account earns 1/2% per month, how much will Carol have for her annual post-Christmas shopping spree? (You may assume Carol withdraws the entire amount December 31.)

6. Solution; Begin of Period F F = 200(F/A, 0.5, 12) = $2,467 0 1 2 12

7. 0 1 12 Solution; Begin of Period F F = 200(F/A, 0.5, 12) = $2,467 F 0 1 2 12

8. Solution; Begin of Period F F = 200(F/A, 0.5, 12) = $2,467 F = 200(F/A, 0.5, 12)(F/P, 0.5, 1) = 2,467(1.005) = $2,479 F 0 1 2 12 0 1 12 0 1 2 12

9. Balloon Payment A company borrows $10,000 at a nominal annual interest rate of 12% compounded monthly. The company desires to repay the loan in 18 equal monthly payments, with the first payment starting 1 month from now. a. What should be the size of each payment? b.The company decides to pay off the balance of the loan in the 12th month. What should the size of the 12th payment be? (Note: the first 11 payments are as computed in Part a)

10. Solution; Balloon Payment 1 2 3 18 10,000 A A = 10,000(A/P, 1, 18) = 10,000 (0.0610) = $610

11. Solution; Balloon Payment 1 2 3 12 18 10,000 610 10,000= 610 (P/A, 1, 11) + X(F/P, 1, 12) X

12. Solution; Balloon Payment 1 2 3 12 18 10,000 610 10,000= 610 (P/A, 1, 11) + X(F/P, 1, 12) = 610(10.3676) + X (.8963) X

13. Solution; Balloon Payment 1 2 3 12 18 10,000 610 10,000= 610 (P/A, 1, 11) + X(F/P, 1, 12) = 610(10.3676) + X (.8963) X= 10,000 - (610)(10.3676).8963 = $4,101 X

14. Bond Issues Stu can buy a 7-year bond issued 1 year ago. The face value of the bond is $1,000 paying 8% annually. How much should Stu pay for the bond if he requires 12% return on his money?

15. Bond Issues 80 80 80 1,000 1 2 3 4 5 6 7 P

16. Bond Issues 80 80 80 1,000 1 2 3 4 5 6 7 P P = 80(P/A, 12, 6) + 1,000(P/F, 12, 6) = 80(4.1114) + 1,000(.5066) = $835.54