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16 May, 23:25

A 45-year old man puts $1000 in a retirement account at the end of each quarter until he reaches the age of 60 and makes no further deposits. If the account pays 8% interest compounded quarterly, how much will be in the account when he retires at 65?

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  1. 16 May, 23:50
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    The account will have $292,526.3494 by the time he retired

    Step-by-step explanation:

    The expression for the total amount earned from the investment is;

    A=P (1+r/n) ^nt

    where;

    A=future value of investment

    P=present value of investment

    r=annual interest rate

    n=number of periods

    t=number of years

    In our case;

    P=deposits $1000 every 3 months for 15 years

    A year has 4 periods

    The present value, P=1000*4*15=$60,000

    r=8%=8/100=0.08

    n=4

    t = (65-45) = 20 years

    replacing;

    A=60,000 (1+0.08/4) ^ (4*20)

    A=60,000 (1.02) ^80

    A=292,526.3494

    The account will have $292,526.3494 by the time he retired
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