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5 December, 07:04

You borrowed $1,500 at 6% compounded annually. your payments are $90 at the end of each year. how many years will you make payments on the loan?

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  1. 5 December, 07:10
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    Given the formula for future value annuity:

    FV of annuity=P[ (1+r) ^n-1]/r

    where:

    P=principle

    r=rate

    n=time

    the time taken to repay the loan will be:

    1500=90[ (1+0.06) ^n-1]/0.06

    90=90[ (1+0.06) ^n-1]

    1 = (1+0.06) ^n-1

    1+1 = (1+0.06) ^n

    2=1.06^n

    introduce natural log

    ln2=nln1.06

    n=ln2/ln1.06

    n=11.8957=12 years

    the answer is 12 years.
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