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?

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slicergiza slicergiza · Answer 1 · 2019-12-11T07:13:23+01:00

Answer:

$ 9486.3354

Step-by-step 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 = [tex]\frac{0.01}{12}[/tex]

Number of months, n = 36,

Thus, total payment,

[tex]A=P(1+r)^n[/tex]

[tex]=P(1+\frac{0.01}{12})^{36}[/tex]

[tex]=P(1.0304)[/tex]

∵ A = $7920,

[tex]\implies P(1.0304) = 7920[/tex]

[tex]P=\frac{7920}{1.0304}=7686.3354[/tex]

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

= 7686.3354 + 1800

= $ 9486.3354

≈ $ 9486.36