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Thread: Should I be using t = I/Pr ?

  1. #1
    Jul 2014

    Should I be using t = I/Pr ?

    Hello. In a maturity value interest question I am not quite sure what formula to use to get time, and also what measurement I should be using for the time (days, months, etc)

    The question is:

    Calculate the time period of an investment in a mutual fund that matured to $250,000 yielding an interest of $75,000 at 6% compounded semi-annually? Please round your answer up to the nearest month.

    What I have done so far:

    S = P + I so P=S-I P = 250,000-75,000 = 175,000

    Now that I have S, P, and I, time is required.

    I tried using t=i/pr which gets me 75,000 / [250,000*0.06] which = 5

    Is that 5 years? Another thing is that equation didnt account for the semi annual compounding :s

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  2. #2
    MHF Contributor ebaines's Avatar
    Jun 2008

    Re: Should I be using t = I/Pr ?

    There are a few things wrong here. First, the formula t = i/pr works for simple interest only, not compound interest. And second, the denominator of that should be the amount invested, which was 175K. So that formula would yield t = 75/(175*.06) = 7.14, meaning it would take 7.14 years of simple interest to make the investment reach $250K.

    For compound interest you use: $\displaystyle FV = PV(1+i)^n$ where i is the interest rate per period and n is the number of periods of time. In this case a period is half a year in duration, and so the value for i is 0.06/2. PV is the present (or beginning) value and FV is the future (or ending) value. So you have:

    $\displaystyle 250 = 175(1+\frac {0.06} 2 )^n $

    Do you know how to solve for n? Hint - it requires using logarithms. Once you have a value for n, round up to the next whole number and then multiply by 6 to get the number of months.
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