Question

Stereo Inc. sells a stereo system for $100 down and monthly payments of $80 for the next 4 years. If the interest rate is 3% per month, find:
a) The cost of the stereo.
Answer = $  
b) The total amount of interest paid.
Answer = $

Answer 1

a)

The payment R = $80

Interest is 3% per month so i = 0.03/12 = 0.0025

n = 12*4=48

Use the formula for the present value of an annuity

P = R*[1-(1+i)^-n] / i

P = 80[(1-(1+0.0025)^(-48))/0.0025] = 3614.296 ? 3614.30

Since there was down payment of $100, the cost of the stereo will be

$3614.30 + $100 = $3714.30

The cost of the stereo is $3714.30

b)

Since a payment of $80 was paid each month for 48 months, the total of the payments will be 48($80) = $3840

From the part a) the cost of the stereo system will be $3614.30

Therefore the total amount of interest paid will be

$3840 – $3614.30 = $225.7

The total amount of interest paid will be $225.7