Chapter 2 Solutions 1 TM 661Chapter 2 Solutions 1 # 9) Suppose you wanted to become a millionaire at retirement. If an annual compound interest rate of 8% could be sustained over a 40-year period, how much would have to be deposited yearly in the fund in order to accumulate $1 million. Soln: A = F(A/F, I, 40) = 1,000,000 (A/F, 8, 40) = 1,000,000 ( ) = 3,860 A= 1,000,000 (A/F, 10, 40) = 1,000,000 ( ) = 2,259 A= 1,000,000 (A/f, 12, 40) = 1,000,000 ( ) = 1, A A A A A F = 1,000,000

Chapter 2 Solutions 2 TM 661 Chapter 2Solutions Kim deposits $1,000 in a savings account; 4 years after the deposit, half of the account balance is withdrawn. $2,000 is deposited annually for an 8-year period, with the first deposit occurring 2 years after the withdrawal. The total balance is withdrawn 15 years after the initial deposit. If the account earned interest of 8% compounded annually over the 15 year period, how much was withdrawn at each withdrawal point? Soln: At year 4, value in the account is given as F = 1,000(F/P, 8, 4) = 1,000(1.08) 4 = 1,360 Leaving half in the account leaves 680 in period 4. Then in year 15, the total amount in the account is given by = 680(F/P, 8, 11) + 2,000(F/A, 8, 8)(F/P, 8, 2) = 680(1.08) ,000( )(1.08) 2 = $ 26,399 1,000 2,000 2,000 2, F 500(1.08) 4

Chapter 2 Solutions 3 TM 661Chapter 2Solutions 3 27) Dr. Shieh deposits $3,000 in a money market fund. The fund pays interest at a rate of 12% compounded annually. Just 3 years after making the single deposit, he withdraws one third the accumulated money in his account. Then 5 years after the initial deposit, he withdraws all of the accumulated money remaining in the account. How much does he withdraw 5 years after his initial deposit? Soln: Amount accumulated by year 3. F= 3,000(F/P, 12, 3) = 3,000 (1.12) 3 = 4,215 Withdrawing 1/3 leaves $2,810 which then earns interest for two more years F 5 = 2,810 (F/P, 12, 2) = 2,810 (1.12) 2 = $3,525 F 1/3 accum. 3,

Chapter 2 Solutions 4 TM 661Chapter 2 Solutions 5 47)A person borrows $10,000 and wishes to pay it back witn 9 equal annual payments. What will the payments be if the interest used is 12% compounded (a) annually, (b) semi-annually, and (c) continuously? Soln: a) i eff = 12% A = 10,000(A/P, 12, 9) = 10,000 (0.1877) = $1,877 b) i eff = (1+.06) =.1236 A = 10,000(A/P, 12.36, 9) = 10,000 (0.1903) = $1,903 c) i eff = e =.1275 A = 10,000(A/P, 12.75, 9) = 10,000 (0.1931) = $1,931 or = 10,000(A/P, 12, 9)cont = 10,000(0.1931)formula p. 61 or table Appendix B, p. 450 = $1, A 15,000

Chapter 2 Solutions 5 TM 661Chapter 2 Solutions 8 67)Ms. Torro-Tamos borrows $7,000 and repays the loan with 4 quarterly payments of $600 during the first year and 4 quarterly payments of $1,500 during the second year. Determine the effective interest rate for this transaction. Soln: 7,000 = 600 (P/A, i, 4) + 1,500 (P/A,i, 4)(P/F, i, 4) The quarterly interest rate is roughly 3.5% per quarter. i eff = ( ) =.1475 = 14.75% 7, ,