Question

Help me please

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

$4700 x 1.07^3

= $5757.70

Answer 2

Answer: each monthly payment is $145.3

Cumulative interest paid is $530.8

Explanation:

We would apply the periodic interest rate formula which is expressed as

P = a/[{(1+r)^n]-1}/{r(1+r)^n}]

Where

P represents the monthly payments.

a represents the amount of the television.

r represents the annual rate.

n represents number of monthly payments. Therefore

a = $4700

r = 0.07/12 = 0.0058

n = 12 × 3 = 36

Therefore,

P = 4700/[{(1+0.0058)^36]-1}/{0.0058(1+0.0058)^36}]

4700/[{(1.0058)^36]-1}/{0.0058(1.0058)^36}]

P = 4700/{1.23 -1}/[0.0058(1.23)]

P = 4700/(0.23/0.007134)

P = 4700/32.34

P = 145.3

The total amount paid in 3 years is

145.3 × 36 = $5230.8

Cumulative interest paid is

5230.8 - 4700 = $530.8