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November 20th, 2017, 08:33 PM  #1 
Senior Member Joined: Apr 2008 Posts: 192 Thanks: 3  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. 
November 21st, 2017, 01:02 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,959 Thanks: 1604 
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. 
November 21st, 2017, 11:07 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,163 Thanks: 867 
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 12:42 PM. 

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