MATH COLLEGE ALGEBRA/BUSN - PRACTICE EXAM #3 - FALL DR. DAVID BRIDGE

Transcription

1 MATH 15 - COLLEGE ALGEBRA/BUSN - PRACTICE EXAM # - FALL DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the simple interest. Round to the nearest cent. 1) $500 at 11% for years Interest = $15.15 Interest = $16.50 Interest = $ Interest = $18. 2) $180 at 19% for 2 2 years Interest = $69.92 Interest = $19.68 Interest = $98. Interest = $ ) $680 at 10% for 2 months Interest = $16.00 Interest = $11. Interest = $11. Interest = $.00 Find the present value of the future amount. Round to the nearest cent. Assume simple interest. ) $22,000 for 9 months; money earns 11% $20,96.89 $ $19, $20,2. 5) $500 for 2 months; money earns 6% $.95 $97.51 $95.05 $71.70 Solve the problem. Assume simple interest. 6) Allan borrowed $500 from his father to buy a car. He repaid him after 6 months with simple interest of %. Find the total amount he repaid. $ $ $5.75 $ ) A company has ordered 12 new personal computers at a cost of $1500 each. They will not be delivered for months. What amount should the firm deposit in an account paying 7.2% simple interest to have enough money to pay for them? $ $17,67.25 $17, $17, Find the compound amount for the deposit. Round to the nearest cent. 8) $11,000 at % compounded annually for 5 years $1,8.18 $12, $1, $12,868. 9) $000 at 8% compounded semiannually for 6 years $ $ $67.50 $ ) $1000 at % compounded quarterly for years $ $ $100. $ Find the compound interest earned by the deposit. Round to the nearest cent. 11) $15,000 at % compounded annually for 19 years $11,02.59 $ $ $10, ) $11,000 at % compounded semiannually for 5 years $11.89 $208.9 $ $ ) $00 at 5% compounded quarterly for years $60.00 $6.0 $6.05 $15.19

2 Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 1) % compounded semiannually.0%.0%.00%.02% 15) 9% compounded quarterly 9.8% 9.00% 9.1% 9.20% 16) 2% compounded monthly 0.27% 1.02% 2.02% 2.01% Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated. 17) $7000 at 11% compounded annually for 9 yr $17, $07.9 $26.5 $ ) $5000 at 6% compounded semiannually for 9 yr $ $ $ $ ) $6800 at 7% compounded quarterly for yr $ $ $87.79 $ Solve the problem. Round to the nearest cent. 20) June made an initial deposit of $2000 in an account for her son. Assuming an interest rate of 12% compounded quarterly, how much will the account be worth in 17 years? $1, $1, $1,91.86 $ ) A small company borrows $5,000 at 9% compounded monthly. The loan is due in years. How much interest will the company pay? $5, $10, $10,61.6 $10, Solve the problem. 22) A bank gives you two options to choose from for your investments: Option A: 6% annual interest rate compounded yearly; and Option B: 5.9% annual interest rate compounded quarterly. Decide which is the better investment at the end of 2 years. Option A Option B 2) Mark and Kate are establishing a fund for their son's college education. What lump sum must they deposit in an account that gives 7% annual interest rate, compounded monthly, in order for them to have $70,000 in the fund at the end of 10 years? $,81.7 $9,07.7 $6,11.7 $7, ) James purchased a bond for $500, and sixteen months later he sold it for $00. What annual rate would he have to earn in a savings account compounded monthly, to earn the same money on his investment? 17.0% 16.29% 15.5% 17.5% 25) $28 is deposited into a savings account at 7% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $61? 9 years 1 years 8 years 6 years

3 26) You have money in an account at 7% interest, compounded annually. To the nearest year, how long will it take for your money to triple? 2 years 10 years 16 years 1 years Find the value. s 27) s 28) Find the future value of the ordinary annuity. Interest is compounded annually, unless otherwise indicated. 29) R = $100, i = 0.0, n = 7 $66.8 $ $ $ ) R = $7500, i = 5% interest compounded semiannually for 8 years $5,51.69 $1,89.5 $15,51.69 $211, ) R = $2500, i = % interest compounded quarterly for 16 years $217,96.11 $222,615.7 $112, $72,615.7 Find the periodic payment that will render the sum. 2) S = $65,000, interest is 8% compounded annually, payments made at the end of each year for 12 years $ $25.18 $ $90.96 ) S = $6,000, interest is 18% compounded monthly, payments made at the end of each month for years $ $ $12, $97.01 ) S = $5,000, interest is 12% compounded quarterly, payments are made at the end of each quarter for 5 years $ $ $1972. $289.6 Solve the problem. 5) If Bob deposits $5000 at the end of each year for years in an account paying 8% interest compounded annually, find the amount he will have on deposit. $11,22.00 $10,00.00 $22,50.56 $16, ) At the end of every months, Teresa deposits $100 into an account that pays 5% compounded quarterly. After years, she puts the accumulated amount into a certificate of deposit paying 7.5% compounded semiannually for 1 year. When this certificate matures, how much will Teresa have accumulated? $ $ $188.1 $ ) Which of the following investments is larger after 18 years? $5000 is deposited annually and earns.5% interest compounded annually. $00 is deposited monthly and earns.5% interest compounded monthly. 8) Mark wants to start an IRA that will have $70,000 in it when he retires in 2 years. How much should he invest quarterly in his IRA to do this if the interest is 1% compounded quarterly? $ $ $ $568.1

4 Find the value. a 9) a 0) Find the present value of the ordinary annuity. 1) Payments of $590 made annually for 1 years at 6% compounded annually $96. $58.05 $ $ ) Payments of $55,000 made semiannually for 12 years at 12% compounded semiannually $689, $87,81.50 $70, $690,269.6 ) Payments of $96 made quarterly for 10 years at 8% compounded quarterly $ $26.1 $92.5 $91.76 Find the lump sum deposited today that will yield the same total amount as this yearly payment (made at the end of each year for 20 years at the given interest rate, compounded annually). ) $600 at % $ $ $ $ ) $15,100 at 8% $15,01.6 $18, $151,25.68 $18,25.99 Find the payment necessary to amortize the loan. 6) $10,000; 6% compounded annually; 7 annual payments $ $1791. $20.6 $ ) $12,000; 9% compounded semiannually; 10 semiannual payments $ $ $151.8 $ ) $1900; 12% compounded quarterly; 8 quarterly payments $2.02 $ $82.8 $270.7 Find the monthly house payment necessary to amortize the following loan. 9) In order to purchase a home, a family borrows $127,000 at 8.% for 0 yr. What is their monthly payment? Round the answer to the nearest cent. $ $878.2 $ $ Solve the amortization problem. Round to the nearest cent. 50) The monthly payments on a $8,000 loan at 1% annual interest are $ How much of the first monthly payment will go toward the principal? $798.6 $ $18.81 $ ) The monthly payments on a $86,000 loan at 11% annual interest are $ How much of the first monthly payment will go toward the principal? $ $ $189.9 $788.

5 52) The monthly payments on a $7,000 loan at 1% annual interest are $ How much of the first monthly payment will go toward interest? $ $127.1 $ $ Solve the problem. 5) Tasha borrowed $9000 to purchase a new car at an annual interest rate of 10%. She is to pay it back in equal monthly payments over a 5 year period. What is her monthly payment? $15.00 $75.00 $ $ ) Julio buys a bike which has a cash price of $250. He agrees to take a one-year loan for the entire amount at 27%, payable in 12 installments. After 8 of the 12 payments, he gets some birthday money and decides to pay off his loan. Find the unpaid balance. $ $90.8 $88.72 $ ) Find the least amount that could be deposited in a bank account today at 12% compounded quarterly to allow $650 withdrawals at the end of each quarter for 9 years? $1, $29,12.7 $1, $1,08.71 *** SKIP THIS SECTION *** Solve the system of two equations in two variables. 56) x - y = -29-5x - 5y = -55 (2, 9) (-, 9) (, 8) No solution 57) -6x + 8y = 56 -x - 2y = -1 (0, 7) (-1, 8) No solution (0, 8) 58) -x - 10 = 6y -2x - y = 5 (-7, ) (-7, ) No solution (-8, ) 59) x - 2y = 9 15x - 10y = 18 (1, 0) (0, -.5) No solution (1, -) 60) x + 5y = 6x + 10y = 8-5 y +, y for any real number y - 1, 1, 0 No solution *** SKIP THIS SECTION *** Multiply both sides of each equation by a common denominator to eliminate the fractions. Then solve the system. 61) 1 x + 1 y = - x - y = - (6, -2) (-7, -2) No solution (-6, -)

6 62) x 8 - y 5 = 80 x 7 + y 5 = 7 5 1, 1 2 2,, 1 2 2, 1 Solve the problem. 6) What is the size of the matrix? x x 6) What is the size of the matrix? x x 1 65) What is the size of the matrix? Perform the indicated operation where possible ) ) ) Not defined Perform the indicated operation. 69) Let A = Find 5A

7 70) Let C = Find 1 2 C ) Let C = and D = Find C - D ) Let A = - 2 and B = 1 0. Find 2A + B Solve the problem. 7) Barnes and Able sell life, health, and auto insurance. Sales for May and June are given in the matrices. M = Life Health Auto 20,000 15, , ,000 Able Barnes J = 70, ,000 0,000 2,000 2,000 Able Barnes Find the matrix that would give total sales for the months of May and June. 90, ,000 90,000 15,000 8,000 70, ,000 70,000 2,000 9,000 90,000 15,000 8,000 70,000 2,000 2, ,000 9,000 87,000

8 7) Carney and Dobler sell home and mortgage insurance. Their sales for the months of May and June are given in the matrices. M = Home Mortgage 22,000 5,000 Carney 19,000 27,000 Dobler J = 25,000 2,000 1,000 21,000 Carney Dobler Find the matrix that would give the change in sales from May to June ) The matrix shows the average number of wax and buff treatments each of workers in a car wash can do in a day. Give the matrix that shows what each worker can do in days. Wax Buffs 6 10 T = Ford Morton Porter Find the order of the matrix product AB and the product BA, whenever the products exist. 76) A is x, B is x. AB is x 6, BA is x 6. AB is 1 x 1, BA is 1 x 1. AB is x, BA is x. AB is 6 x, BA is 6 x. 77) A is 2 x 1, B is 1 x 2. AB is 2 x 2, BA is 1 x 1. AB is 1 x 1, BA is 2 x 2. AB is 2 x 2, BA is nonexistent. AB is nonexistent, BA is 1 x 1. 78) A is 2 x 1, B is 1 x 1. AB is 2 x 2, BA is 1 x 1. AB is 2 x 1, BA is nonexistent. AB is 1 x 2, BA is 1 x 1. AB is nonexistent, BA is 1 x 2. Given the matrices A and B, find the matrix product AB. 79) A = 0-2, B = -2 0 Find AB

9 80) A = 7-9 8, B = Find the dot product of A and B Nonexistent 81) A = 9-1 2, B = 1. Find the dot product of A and B Nonexistent 82) A = , B = Find the dot product of A and B Nonexistent 8) A = , B = ) A = -1 1, B = AB is not defined ) A = , B = AB is not defined ) A = , B = AB is not defined

10 ) A = 0 1 0, B = AB is not defined. 88) A = , B = x y x y x y AB is not defined. 89) A = , B = AB is not defined.

11 Answer Key Testname: MATH PRACTICE EXAM # 1) C 2) D ) C ) D 5) C 6) B 7) C 8) A 9) D 10) B 11) A 12) B 1) B 1) D 15) C 16) C 17) D 18) C 19) B 20) B 21) B 22) B 2) A 2) C 25) A 26) C 27) D 28) D 29) C 0) C 1) B 2) B ) D ) C 5) D 6) B 7) A 8) A 9) A 0) A 1) C 2) D ) C ) C 5) D 6) B 7) B 8) B 9) D 50) C 51) C 52) C 5) C 5) B 55) A 56) C 57) A 58) B 59) C 60) A 61) D 62) D 6) D 6) B 65) D 66) C 67) C 68) C 69) A 70) D 71) D 72) B 7) B 7) D 75) D 76) C 77) A 78) B 79) B 80) B 81) A 82) D 8) B 8) A 85) B 86) A 87) B 88) C 89) D