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March 27, 2017

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An amount of $3000 was deposited in a bank at a rate of 2% annual interest compounded quarterly for 3yrs. The rate then increased to 3% annual interest and ws compounded quarterly for the next 3 yrs. If no money was withdrawn what was the balance at the end of this time?

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    $3000 at 2% for 3 years, followed by 3% for 3 years, all compounded quarterly.

    The basic equation for the future value A (accumulated amount) of a principal P at r% interest per period for n periods is:
    A=PR^n
    where R=1+r
    At the end of the three years at 2%, the amount is reinvested at 3%, so the calculated A becomes P for the second part.

    First three years:
    No. of periods, n = 4*3 = 12 quarters
    interest per period, 1+2%/4=1.005
    Principal = $3000
    Amount at the end of three years:
    A = PR^n = 3000*1.005^12
    = 3000*1.06168
    = $3185.03

    For the second part,
    P=$3185.03
    R=1+3%/4=1.075
    n=12
    A=PR^n=3185.03*1.075^12=?

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