I need help with finding monthly payments

label Business & Finance
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schedule 1 Day
account_balance_wallet $5

A commercial bank will loan you $51,084 for 5 years to buy a car. The loan must be repaid in equal monthly payments at the end of the month. The annual interest rate on the loan is 16.47 percent of the unpaid balance. What is the amount of the monthly payments?

Sep 1st, 2015

Thank you for the opportunity to help you with your question!

Loan: 51084

Period 5 Years

Interest is 16.47 on reducing balance

Monthly Payment?

The total Months  5 X 12= 60 Months

The monthly repayment will be 51084/60

=$ 851.4  = Interest which we calculate as

Factor it from being annual to monthly

16.47%/12 = 0.013725 

Remember this is monthly

using the formula

M = P * ( J / (1 - (1 + J)-N)). where
  • M = payment amount
  • P = principal, meaning the amount of money borrowed
  • J = effective interest rate. Note that this is usually not the annual interest rate; see below for an explanation.
  • N = total number of payments
then

Because of time factor I will post the rest in a moment. Thanks





Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 1st, 2015

Factoring the values in to the fomula gives:

M = P * ( J / (1 - (1 + J)-N)).

51084 x ( 0.013725 / (1-(1+ 0.013725)^-60))

= 51084 x ( 0.013725/ ( 1- 0.4413576 ))

=51084 x 0.024568 

= $1255.032

Sep 1st, 2015

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