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

(a). $1465.42

(b). $214.58

Explanation:

We have been given that installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. The interest rate is 1.25% per month on the unpaid balance.

(a) To find the cost of the TV, we will use monthly payment formula.

`R=(Pi)/(1-(1+i)^(-n))`, where,

R = Periodic payment,

P = Loan amount,

i = Monthly interest rate in decimal form,

n = Number of total payments.

`n=3* 12=36`

`1.25\%=(1.25)/(100)=0.0125`

`30=(P*0.0125)/(1-(1+0.0125)^(-36))`

`30=(0.0125P)/(1-(1.0125)^(-36))`

`30=(0.0125P)/(1-0.6394091578134724264)`

`30=(0.0125P)/(0.3605908421865275736)`

`10.817725265595827208=0.0125P`

`0.0125P=10.817725265595827208`

`P=(10.817725265595827208)/(0.0125)`

`P=865.41802124766617664`

`P\approx 865.42`

We know that total cost of TV would be equal to down payment plus amount of loan that is:

`865.42+600=1465.42`

Therefore, the total cost of the TV would be $1465.42.

(b). First of all, we need to find total amount paid in 3 years by multiplying amount of each monthly payment by 36 (3 years equal to 36 months).

`\$30* 36=\$1080`

To find the total amount of interest paid, we will subtract amount of loan from total payment.

`\$1080-\$865.42=\$214.58`

Therefore, the total amount paid in interest would be $214.58.