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3. A lender offers a $ 4000 loan for 3 months at 6% interest. (a) What is the monthly interest rate for the loan? (b) Use the formula to calculate x, the monthly payment for the loan.  x = P(1-j)/j(1-j^m) where j=1/1+i

Guest Oct 18, 2017
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The interest rate of 6% is not specific enough. Is it APR (Annual Percentage Rate), or is it just for the 3 months stated. Also, how often is it compounded? Is it daily, weekly monthly, quarterly,  semi-annually, annually.....etc. It is very important that the interest rate be quoted very accurately, otherwise, you will get the wrong result.

As a result, I'm going to assume that your 6% interest is annual and compounded monthly. Also, I don't quite understand your formula for a monthly payment. Therefore, I'm going to use a familiar formula that is "universal" !!.

PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}, Where R=Interest rate per period, N=number of periods, PMT=periodic payment, PV=Present value.

 

Under my assumption, your monthly interest rate would be =6% / 12 = 1/2%.

 

PMT =4,000 x 0.06/12{[1 + 0.06/12]^3 / [1 + 0.06/12]^3 - 1}

PMT =20 x {[1.005]^3 / [1.005]^3 - 1}

PMT = 20 x {1.015075125 / (1.015075125 - 1)}

PMT = 20 x {1.015075125 / 0.015075125}

PMT = 20 x                67.33444167........

PMT =$1,346.69 - This is the payment for 3 months on $4,000 loan @ 6% compounded monthly.

Guest Oct 18, 2017
edited by Guest  Oct 18, 2017

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