# Math

The Bennetts spend \$10,000.00 on a home improvement project. They make the purchase with a credit card that has a 9% APR. They decide to make \$150.00 monthly payments.

How many months will it take to pay off the credit card balance?

Can someone show me a step by step on how to solve or a formula

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1. Wow, first of all, where do you find a credit card that charges 9% ???

This is the formula:
Present Value = payment( 1 - (1+i)^-n)/i
where i is the interest rate per period expressed as a decimal (in this case period is 1 month)
n is the number of interest periods

so
i = .09/12 = .0075
n = ?? (we don't know that)
payment = 150
PV = 10000
10000 = 150(1 - 1.0075^-n)/.0075
75 = 150(1 - 1.0075^-n)
1/2 = 1 - 1.0075^-n
1.0075^-n = 1/2
we know have to use logs, take log of both sides and use log rules
-n log 1.0075 = log .5
-n = log .5/log 1.0075 = -92.76...
n = appr 93 interest periods, which were months

I will take 92 full payments of 150, plus a partial final payment in the 93rd month

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Reiny

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