Question

Installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. If the interest rate is 1.25% per month on the unpaid balance, find (a) the cost of the TV (b) the total amount of interest paid

Answer 1

Answer:

a) $ 1465.418

b) $ 214.582

Step-by-step explanation:

Since, the monthly payment formula of a loan is,

$P=\frac{PV(r)}{1-(1+r)^{-n}}$

Where, PV is the principal amount of the loan,

r is the monthly rate,

n is the total number of months,

Here, P = $ 30, r = 1.25 % = 0.0125, n = 36 ( since, time is 3 years also 1 year = 12 months )

Substituting the values,

$30=\frac{PV(0.0125)}{1-(1+0.0125)^{-36}}$

By the graphing calculator,

$PV=865.418$

a) Thus, the cost of the TV = Down Payment + Principal value of the loan

= $ 600 + $ 865.418

= $ 1465.418

b) Now, the total payment = Monthly payment × total months

= 30 × 36

= $ 1080

Hence, the total amount of interest paid = total payment - principal value of the loan

=  $ 1080 - 865.418

=  $ 214.582.