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FE Practice Problems w/ Solutions 4-114 1 If you borrow $3,000 at 6% simple interest per year for seven years, how much will you have to repay at the end of seven years? [4.4] (a) $3,000 (b) $4,511 (c) $1,260 (d) $1,511 (e) $4,260 Solution: I = (P)(N )(i ) = (3, 000)(7)(0.06) = $1, 260 F = P + I = 3, 000 + 1, 260 = $4, 260 Select (e) 4-115 When you were born, your grandfather established a trust fund for you in the Cayman islands. The account has been earning interest at the rate of 10% per year. If this account will be worth $100,000 on your 25th birthday, how much did your grandfather deposit on the day you were born? [4.8] (a) $4,000 (b) $9,230 (c) $10,000 (d) $10,150 (e) $10,740 Solution: ( ) P = 100,000 P ,10%, 25 = 100,000 (0.0923)= $9, 230 F Select (b) 4-116 Every year you deposit $2,000 into an account that earns 2% interest per year. What will be the balance of your account immediately after the 30th deposit? [4.9] (a) $44,793 (b) $60,000 (c) $77,385 (d) $81,136 (e) $82,759 Solution: ( ) F = 2,000 F , 2%,30 = 2,000 (40.5681)= $81,136 A Select (d) 1 Problems choosen from Engineering Economy, 13th Edition, Sullivan, W.G., et.al., Prentice-Hall, 2006 D:\106738382.doc Page 1 of 4 FE Practice Problems w/ Solutions 4-117 Your monthly mortage payment (principal plus interest) is $1,500. if you have a 30-year loan with a fixed interest rate of 6% compounded monthly, how much did you borrow from the bank to purchase your house? Select the closest answer. [4.17] (a) $154,000 (b) $180,000 (c) $250,000 (d) $300,000 (e) $540,000 Solution: i = 6% = 1 2 % per month (0.5%) mo 12 N = 30 ´ 12 = 360 months é (1.005)360 - 1 ù ú= 1,500 [166.7916] P P = 1,500 , 0.5%,360 = 1,500 êê 360 ú A êë(0.005)(1.005) ú û P = $250,187 per month ( ) Select (c) 4-118 Condider the following sequence of year-end cash flows: EOY Cash Flow 1 $8,000 2 $15,000 3 $22,000 4 $29,000 5 $36,000 What is the uniform annual equivalent if the interest rate is 12% per year? [4.13] (a) $20,422 (b) $17,511 (c) $23,204 (d) $22,000 (e) $12,422 Solution: A = 8, 000 G = 7, 000 ( ) ATotal = 8, 000 + 7, 000 A ,12%,5 G 1.7746 ATotal = $20, 422 Select (a) D:\106738382.doc Page 2 of 4 FE Practice Problems w/ Solutions 4-119 A cash flow at time zero (now) of $9,982 is equivalent to another cash flow that is an end-of-year annuity of $2,500 over five years. Each of these two cash flows series is equivalent to a third series, which is a uniform gradient series. What is the value of G for this third series over the same five year time interval? [4.13] (a) $994 (b) $1,150 (c) $1,250 (d) $1,354 (e) not enough information Solution: ( ) 9,982 = 2,500 P , i ',5 A P , i ',5 = 9,982 = 3.9928 A 2,500 i ' = 8% per year ( ) ( ) 9,982 = G P ,8%,5 G 7.372 9,982 G= = $1,354 7.372 Select (d) 4-120 What is the monthly payment on a loan of $30,000 for seven years at a nominal interest rate of 9% compounded monthly? [4.17] (a) $4,416 (b) $258 (c) $483 (d) $2,700 (e) $225 Solution: i = 9% = 3 % per month mo 12 4 N = 7 ´ 12 = 84 months é(0.0075)(1.0075)84 ù ú= 30, 000 [0.0161] 3 A A = 30, 000 , %,84 = 30, 000 êê ú 84 P 4 êë (1.0075) - 1 ú û A = $483 per month ( ) Select (c) D:\106738382.doc Page 3 of 4 FE Practice Problems w/ Solutions 4-121 A bank advertises mortgages at 12% compounded continuously. What is the effective annual interest? [4.18] (a) 12.36% (b) 12.55% (c) 12.75% (d) 12.68% (e) 12.00% Solution: r = 12% i = er - 1 = e0.12 - 1 = 0.1275 or 12.75% compounded annually Select (c) 4-122 If you borrow $5,000 to buy a car at 12% compounded monthly, to be repaid over the next four years, what is your monthly payment? [4.17] (a) $131 (b) $137 (c) $1,646 (d) $$81 (e) $104 Solution: i = 12% = 1% per month mo 12 N = 4 ´ 12 = 48 months ( ) A = 5, 000 A ,1%, 48 = 5, 000 (0.0263) P A = $131.50 per month Select (a) 4-123 If you invest $7,000 at 12% compounded continuously, h ow much would it be worth in three years? [4.18] (a) $9,449 (b) $4,883 (c) $10,033 (d) $9,834 (e) $2,520 Solution: ( ) ,12%,3 = 7, 0000e( )( ) P = 7, 000e0.36 = 7, 000 (1.4333) = $10, 033 F = 7, 000 F 0.12 3 Select (c) D:\106738382.doc Page 4 of 4