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27 January, 00:55

Tom's stockbroker offers an investment that is compounded continuously at an annual interest rate of 3.7%. If Tom wants a return of $25,000, how long will Tom's investment need to be if he puts $8000 initially? Give the exact solution in symbolic form and then estimate the answer to the tenth of a year.

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  1. 27 January, 00:58
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    It'll take 38.3 years to obtain the desired return of $25,000.

    Step-by-step explanation:

    In order to solve a continuosly coumponded interest question we need to apply the correct formula that is given bellow:

    M = C*e^ (r*t)

    Where M is the final value, C is the initial value, r is the interest rate and t is the time at which the money was applied. Since he wants an return of $25,000 his final value must be the sum of the initial value with the desired return. So we have:

    (25000 + 8000) = 8000*e^ (0.037*t)

    33000 = 8000*e^ (0.037*t)

    e^ (0.037*t) = 33000/8000

    e^ (0.037*t) = 4.125

    ln[e^ (0.037*t) ] = ln (4.125)

    t = ln (4.125) / (0.037)

    t = 1.4171/0.037 = 38.2991

    t = 38.3 years
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