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23 August, 19:03

On january 1, 1980, moises deposited $1850 into a savings account paying 5.6% interest, compounded quarterly. if he hasn't made any additional deposits or withdrawals since then, and if the interest rate has stayed the same, in what year did his balance hit $3700, according to the rule of 72?

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  1. 23 August, 22:18
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    We first calculate for the effective interest of the given nominal interest that is compounded quarterly through the equation,

    ieff = (1 + i/4) ^4 - 1

    Substituting the known values,

    ieff = (1 + 0.056/4) ^4 - 1 = 0.05718

    To determine the future worth of a money invested with an interest that is compounded, the equation is,

    F = P x (1 + ieff) ^n

    where P is the present worth and n is the number of years.

    For this item, we substitute the known terms in the derived second equation

    3700 = (1850) x (1 + 0.05718) ^n

    The value of n is 12.46 years.

    Therefore, the money will be worth $3700 only on 1992.
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