Monthly payment

Question

Stereo Inc. sells a stereo system for $200 down and monthly payments of $70 for the next 3 years. If the interest rate is 1.25% per month, find:

 

a) The cost of the stereo?

 

b) The total amount of interest paid?

Answer 1

The equation to find the monthly payment for an installment loan is called the Equal Monthly Installment (EMI) formula. It is defined by the equation:
Monthly Payment; M = P*r*(1+r)ⁿ/((1+r)ⁿ -1)


r: Interest rate, in decimal form = 1.25/100 = 0.0125
P: principal loan amount (cost of the Stereo minus initial payment down) = x - 200
n: number of payments = 3yrs × 12 monthly payments = 36 payments

M: is given to be 70$

 

70 = (x-200)*(0.0125)*(1+0.0125)³⁶/((1+0.0125)³⁶-1)

 

70 = (0.0125x - 2.5)*(1.0125)³⁶/((1.0125)^{36 -1)}

70 = (0.0125x - 2.5)*(1.564)/(1.564 -1)

70 = (0.0125x - 2.5)*(1.564)/(0.564)

70 = (0.0125x - 2.5)*(2.773)

70 = 0.0347x - 6.9325

70 + 6.9325 = 0.0347x

76.9325 = 0.0347x

76.9325/0.0347 = x

 

2217.08 = x

Answers may vary slightly due to rounding. Cost of the stereo ~ $2217

 

Interest is the amount paid in addition to the amount loaned.

$70 is paid for 36 months = 70*36 = $2520

The amount loaned; P: 2217 - 200 = $2017

 

$2520 - $2017 = $503 interest