Question

Please help!! With step by step

Gary has decided to buy a new flat screen TV system for $4,700 and agreed to make monthly payments
for three years at 7% compounded monthly. How much is each payment? How much will he pay in
cumulative interest?

Answer 1

`R=\$145.12`

Explanation:

Compound Interest

This is a well-know problem were we want to calculate the regular payment R needed to pay a principal P in n periods with a known rate of interest i.

The present value PV or the principal can be calculated with

`P=F_a\cdot R`

Solving for R

`\displaystyle R=(P)/(F_a)`

Where Fa is computed by

`\displaystyle F_a=(1-(1+i)^(-n))/(i)`

We'll use the provided values but we need to convert them first to monthly payments

`i=7\%=7/(12\cdot 100)=0.00583`

`n=3*12=36`

`\displaystyle F_a=(1-(1+0.00583)^(-36))/(0.00583)`

`F_a=32.386`

Thus, each payment is

`\displaystyle R=(4,700)/(32.386)=145.12`

`\boxed{R=\$145.12}`