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18 February, 20:38

If you open an account that compounds quarterly in 2020. In what year will it double the starting amount if it has an APR of 3.2%

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  1. 18 February, 23:28
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    It will double in the year 2063

    Step-by-step explanation:

    Let the amount deposited be $x, when it doubles, the amount becomes $2x

    we can use the compound interest formula to know when this will happen

    The compound interest formula is as follows;

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

    In this question,

    A is the amount which is 2 times the principal and this is $2x

    P is called the principal and it is the amount deposited which is $x

    r is the interest rate which is 3.2% = 3.2/100 = 0.032

    n is the number of times compounding takes place per year which is quarterly which equals to 4

    t is the number of years which we want to calculate.

    Substituting all these into the equation, we have;

    2x = x (1+0.032/4) ^4t

    divide through by x

    2 = (1 + 0.008) ^4t

    2 = (1.008) ^4t

    we use logarithm here

    Take log of both sides

    log 2 = log (1.008) ^2t

    log 2 = 2t log 1.008

    2t = log 2/log 1.008

    2t = 86.98

    t = 86.98/2

    t = 43.49 which is 43 years approximately

    Thus the year the money will double will be 2020 + 43 years = 2063
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