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# how long would it take her to pay off the loan?

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janice is an interior designer and wants to borrow \$5000 so she can attend a trade show in new york. her credit union has offered her an unsecured line of credit at an annual rate of 9.25% compounded weekly .

if she was able to pay back \$200 per month , how long would it take her to pay off the loan ?

Oct 10, 2017

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First, you have to convert the interest rate from compounded weekly to compounded monthly. Then you would use this formula to solve for N, or number of months. Unfortunately, there is no direct solution for N. So, you have to use iteration process to arrive at the answer:

PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}

[1 + 0.0925/52]^52 =1.096823^(1/12)=1.0077312182=9.27746184293% compounded monthly.

200  =5000 x  0.0077312182{[1.0077312182)^N / [1.0077312182]^N - 1}
200 =38.656091{[1.0077312182]^N / [1.0077312182]^N - 1}
5.173828879904 ={[1.0077312182]^N / ([1.0077312182]^N - 1)}, solve for N.
My computer comes up with the number of months, N=27.888 or about 28 months.

Oct 10, 2017