Explanation Given information: The initial investment is $5000, future value is $7500, time duration is 3 years and it is compounded quarterly. Formula used: The formula to calculate compound interest is, A = P ( 1 + r m ) m t Where, P is principal amount. r is interest rate. m is number of conversion per year. t is term (number of years). Calculation: The initial investment is $5000 that means the principal amount is $5000 and the future value is $7500 that means the accumulated amount A is $7500. Here A is $7500, P is $5000, t is 3 years and m is 4 because it is compounded quarterly. To get the rate of interest substitute 7500 for A , 5000 for P , 3 for t and 4 for m into the compound interest formula. 7500 = 5000 ( 1 + r 4 ) 4 × 3 ( 1 + r 4 ) 12 = 1.5 To further simplify the expression take the logarithm on each side. ln ( 1 + r 4 ) 12 = ln ( 1.5 ) 12 ln ( 1 + r 4 ) = ln ( 1.5 ) [ ∵ log b m n = n log b m ] ln ( 1 + r 4 ) = ln ( 1

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 5.3, Problem 16E

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The rate of interest needs to get the given future value on an initial investment.

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Chapter 5.3, Problem 15E

Chapter 5.3, Problem 17E

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Chapter 5 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The rate of interest needs to get the given future value on an initial investment.

Solution Summary: The author explains how the rate of interest needs to get the given future value on an initial investment is approximately 13.75% per year.

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Chapter 5 Solutions