Question

Omar has decided to purchase an $11,000 car. He plans on putting 20% down toward the purchase, and financing the rest at 4.8% interest rate for 3 years. Find his monthly payment.

Answer 1

Answer: $262.95

Step-by-step explanation: confirmed

Answer 2

The monthly payment is $262.95

Explanation:

* Lets explain how to solve the problem

- Omar has decided to purchase an $11,000 car

- He plans on putting 20% down toward the purchase

* Lets find the value of the 20%

∵ The principal value is $11000

∴ the value of the 20% = 20/100 × 11000 = 2200

∴ He will put $2200 down

* Lets find the balance to be paid off on installments

∴ The balance = 11000 - 2200 = 8800

- He financing the rest at 4.8% interest rate for 3 years

* Lets find the rule of the monthly payment

∵
`pmt=((r)/(n)[P(1+(r)/(n))^(nt)])/((1+(r)/(n))^(nt)-1)` , where

- pmt is the monthly payment

- P = the investment amount

- r = the annual interest rate (decimal)

- n = the number of times that interest is compounded per unit t

- t = the time the money is invested or borrowed for

∵ P = 8800

∵ r = 4.8/100 = 0.048

∵ n = 12

∵ t = 3

∴
`pmt=((0.048)/(12)[8800(1+(0.048)/(12))^(3(12))])/((1+(0.048)/(12))^(3(12))-1)`

∴
`pmt=(0.004[8800(1.004)^(36)])/((1.004)^(36)-1)=262.95`

* The monthly payment is $262.95