Question

Lupe made a down payment of $1800 toward the purchase of a new car. To pay the balance of the purchase price, she has secured a loan from her bank at the rate of 10%/year compounded monthly. Under the terms of her finance agreement she is required to make payments of $220/month for 36 months. What is the cash price of the car?

Answer 1

$ 9486.3354

Explanation:

Given,

Payment per month = $ 220,

Number of months = 36,

Total payment = 220 × 36 = $7920,

Let P be the present value of the loan,

Here, annual rate = 10% = 0.01,

So, monthly rate, r =
`(0.01)/(12)`

Number of months, n = 36,

Thus, total payment,

`A=P(1+r)^n`

`=P(1+(0.01)/(12))^(36)`

`=P(1.0304)`

∵ A = $7920,

`\implies P(1.0304) = 7920`

`P=(7920)/(1.0304)=7686.3354`

Hence, the case price of the car = P + down payment

= 7686.3354 + 1800

= $ 9486.3354

≈ $ 9486.36