MATH 1324 Homework 5 Answers
MATH1324 Finite Mathematics · University of Houston
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Complete Solution for MATH 1324 Homework 5
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1 MATH 1324 - Finite Math with Applications Homework 5 (Untimed, 1 Attempt) DUE October 7, 2022 11:59:00 PM! Use the following problem to answer questions 1 and 2. A young man is the beneficiary of a huge trust fund 35 years ago. If they had set aside $25,000, how much will be in the trust now if they could invest the money at 2.5% per year compounded annually? Q1. Identify the type problem. A. Present Value with compound interest (INCORRECT) B. Future Value with compound interest C. Simple Interest D. Future Value with simple interest E. Present Value with simple interest F. None of the above. - Given data o Time period (t) = 35 years o Rate of interest (r) = 2.5% o Principle amount (P) = 25,000 The type of problem is present value with compound interest , so it is option A. Q2. How much money will they have if the interest is compounded semiannually? A. $505,789.33 B. $62,773.32 C. $59,647.50 D. $65.592.11 E. $33,308.30 F. None of the above. - Compound interest semiannually (CI) = P ( 1 + r / 2 100 ) 2 t CI = 25000 ( 1 + 2.5 / 2 100 ) 2 × 35 = 25000 ( 1 + 2.5 200 ) 70 = 59,647.4993 59,647.50 - F = 25000 P = F (1 + i ) - n t = 35 = 25000 ( 1 + 0.025 2 ) 70 r = 2.5% = 0.025 = 59,647.4993 $59,647.50 m = 2 i = r m = 0.025 2 n = mt 2(35) = 70
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2 Use the following problem to answer questions 3 and 4. Corrie bought a new flat screen 70 inch television and a speaker system from a local electronics store on credit. The store will charge 12% per year compounded monthly. Their monthly payments are $174.80 for 3 years. What is the cash price of her purchase? Q3: Identify the type of problem. A. Future Value with compound interest B. Present Value with compound interest C. Present Value of an Annuity D. Future Value of an Annuity E. Future Value with simple interest F. None of the above. - The problem asks us the cash price of Corrie's purchase is the same as the present value of an annuity . An annuity is a fixed amount which is paid over a given period of time. Q4: Answer the question in the problem. A. $4,881.98 B. $5,262.79 C. $4,956.80 D. $3,762.26 E. $4,382.98 F. None of the above. - The present value of an ordinary annuity is given as: o Present value = C [ 1 − ( 1 + i ) − n i ] o C = amount of payment per period o i = interest rate o n = number of payments In this problem o C = $174.80 o i = 12% per year compounded monthly = 12 12 × 100 = 12 1200 = 0.01 o n = 3 × 12 = 36 o Present value = 174.80 [ 1 − ( 1 + 0.01 ) − 36 0.01 ] o $5,262.791 = $5,262.79 E = 174.80 P = E [ 1 −( 1 + i ) − n i ] 174.80 [ 1 − ( 1 + 0.12 12 ) − 36 0.12 12 ] = 174.80 [ 1 − ( 1 + 0.01 ) − 36 0.01 ]
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3 m = 12 = $5,262.79 t = 3 r = 12% = 0.12 i = r m 0.12 12 = 0.01 n = mt 12(3) = 36
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