Explanation Given: A 45-year-old man invests $2500 in the retirement account quarterly till the age of 60. The interest rate is 6%. The annuity is compounded quarterly and it is for 65 years. Formula used: 1. Future value of an ordinary annuity is S = R [ ( 1 + i ) n − 1 i ] . Where, S is the future value; R is the periodic payment; i is the interest rate per period; n is the number of periods. 2. Compound Interest Formula: The future value is A = P ( 1 + i ) n . Where i = r m and n = m t , P is the principal r is the annual interest rate; m is the number of compounding periods per year; n is the number of compounding periods; i is the interest rate per period; t is the time in years. Calculation: Given that, a 45-year-old man deposits $2500 in the retirement account quarterly. Hence the periodic payment is R = $ 2500 . The interest is compounded quarterly, then number of payments made in a year is m = 4 . The 45-year-old man deposits till his age of 60. That is, the annuity is for 60 − 45 = 15 years . Hence, the number of periods is n = m t . That is, 15 × 4 = 60 . It is given that the interest rate is r = 6 % . Then the interest rate per period is, i = r m = 6 % 4 = 0.06 4 = 0.015 Use the above mentioned formula 1 to obtain the future value of the ordinary annuity. Substitute R = $ 2500 , i = 0.015 , and n = 60 in S = R [ ( 1 + i ) n − 1 i ] to find the future value of the ordinary annuity, S = 2500 [ ( 1 + 0

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 5.2, Problem 50E

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To find: The amount in the account in the time of retirement at the age of 65.

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Chapter 5.2, Problem 49E

Chapter 5.2, Problem 51E

Chapter 5 Solutions

Finite Mathematics and Calculus with Applications (10th Edition)

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The amount in the account in the time of retirement at the age of 65.

Solution Summary: The author explains how a 45-year-old man invests 2500 in the retirement account quarterly till the age of 60. The annuity is compounded quarterly and it is for 65 years.

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To find: The amount in the account in the time of retirement at the age of 65.

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Chapter 5 Solutions