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$12$

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ion $2$: Your friend submitted the solution below and got the problem wrong. Identify $r$ error and show all steps in finding the correct solution.

Ruestion:

The Johnson family buys a new furnace and air onditioner unit for $$5,000.$ The purchase is made with a credit card that has a $12\%$ APR. The Johnsons make a $$250$ monthly payment. How many months will it take to pay off the credit card balance?

Your friend's work and answer:

$\{\begin{array}{c}\text{:}N=\frac{-log(1-(f_2)(\frac{k}{M}))}{log(1(f_2))}\end{array}$

$=\frac{-log(1-2)}{log(2)}$

$=\frac{-log(-18)}{lg(2)}$

$=$ ExRDK

Where did your friend make an error?

My friend made an error by incorrectly placing the monthly payment in the numerator instead of the loan amount and used $2$ instead of $0\mathrm{.}12$ for the interest rate.

What is the correct solution? Show all of the stens