Finance homework help

Business & Finance
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2. A small-business owner has a debt of $81, 319.50 at a rate of 10%. The goal is to pay off this debt in 7 years. What should the monthly payment be in order to meet this goal?

Nov 30th, 2015

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Q)  A small-business owner has a debt of $81, 319.50 at a rate of 10%. The goal is to pay off this debt in 7 years. What should the monthly payment be in order to meet this goal?

A)  Understand the equation. In order to calculate the monthly payment, we can rely on a relatively simple equation. The monthly payment equation can be represented as follows:


        r(1+r)^n
M=P------------
        (1+r)^n - 1


These variables represent the following inputs:

  M is your monthly payment.
  P is your principal.
  r is your monthly interest rate, calculated by dividing your annual interest rate by 12.
  n is your number of payments (the number of months you will be paying the loan)
  ^ implies exponent (i.e. 2^3 = 2*2*2 )

For your question the known values are:

  Payments are to be based on making a monthly payment
  P = 81319.50
  r = (10%/12) = (0.1/12) = 0.00833
  n = (7 years * 12 months/year) =(7*12)(years * months/years) = 84 months

        r(1+r)^n
M=P------------
        (1+r)^n - 1

                     0.00833(1+0.00833)^84
M=(81319.50)-------------------------------
                       (1+0.00833)^84 - 1

M=1350.00

Which you can verify with the MS-Excel PMT formula:


Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 30th, 2015

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