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November 20th, 2017, 09:33 PM   #1
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a question about compound interest

How long does it take to pay off 125000 dollars if the annual interest rate is 5.5% and compounded monthly with a monthly payment of $710?

my attempted solution

I use the formula: final amount = principal x (1 + interest rate)^time

final amount=125000 dollars
principal=710dollars/month x 12 months
interest rate=0.055

Now, I plug these values into the formula.

125000=(710x12)(1+0.055)^t

Taking the log on both sides gives

t=log(125000/(710x123))/log(1+0.055)=55 years

The answer key says 30 years.

Is the answer key wrong? Please help me. Thanks a lot.
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November 21st, 2017, 02:02 AM   #2
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You are using the wrong formula.

The answer key is correct if the monthly interest rate is calculated as 1/12 of the annual interest rate and the first repayment is made after 1 month.
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November 21st, 2017, 12:07 PM   #3
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The formula you are using is for the amount of money you will have if you put the principal in an account paying interest at "interest" percent per year. Here, you are paying off a loan at \$710 per month. You need to take into account that the amount still to be paid is reduced each month. For example, at 5.5% annually, the interest for the first month is \$125000(.055)/12 = \$572.92. Of the \$710 monthly payment, only \$710 - \$572.92= \$137.08 applies to the principle, the rest paying for interest. That leaves \$125000 - \$137.08 = \$124862.92 as the principle for the next month. The interest for that month is \$124862.92(0.055)/12 = \$572.29, so \$710 - \$572.29 = \$137.71 applies to the principle. That leaves a principle of \$124862 - \$137.71 = \$124724.29.

Last edited by skipjack; November 21st, 2017 at 01:42 PM.
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