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13 July, 16:18

Suppose $40,000 was invested on January 1, 1980 at an annual effective interest rate of 7% in order to provide an annual (calendar-year) scholarship of $5,000 each year forever, the scholarships paid out each January 1.

(a) In what year can the first $5,000 scholarship be made?

(b) What smaller scholarship can be awarded the year prior to the first $5,000 scholarship?

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  1. 13 July, 17:06
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    a). The first $5,000 will be paid on January 1, 1982

    b). The smaller scholarship that will be received=$2,800

    Explanation:

    a). This can be expressed as follows;

    I=PRT

    where;

    I=Interest amount

    P=Initial value of investment

    R=Annual interest rate

    T=number of years the money is invested for

    In our case;

    I = $5,000

    P=$40,000

    R=7%=7/100=0.07

    T=t

    Replacing;

    5,000=40,000*0.07*t

    5,000=2,800 t

    t=5,000/2,800

    t=1.786 years which will be 2 years since although the first amount will be in 1.7 years, the interest has to be paid on January 1 of the next year

    1980+2=1982

    The first $5,000 will be paid on January 1, 1982

    b). What to receive after 1 year

    I=PRT

    where;

    P=$40,000

    R=7%=7/100=0.07

    T=1

    I = (40,000*0.07*1) = 2,800

    The smaller scholarship that will be received=$2,800
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