Question

Esther pays $532 per month for 6 years for a car. she made a down payment of $3,700. if the loan costs 7.1% per year compounded monthly, what was the cash price of the car?

Answer 1

The cash price of the car is $25,873.44

Explanation:

From the question given, let us recall the following statements

Esther pays $532 per month for 6 years for a car.

She made a down payment of= $3,700.

The loan cost 7.1%

The next step is to to get the cash price of the car.

Now,

R (rate)= $532

r =7.1% =0.071%

Since the down payment is $3,700

Then n=48

P = R (1- (1+i)⁻ⁿ/i = 532 (1-(1+0.071/12)⁻⁴⁸/0.071/12

P =22173.44

We now add it by $3700

The cash price of the car is =$25,873.44

Answer 2

The amortization formula relates the principal and the loan payment by
A = Pi/(n(1 -(1 +r/n)^(-nt)))
You have
532 = P*0.071/(12*(1 -(1 +.071/12)^(-12*6))) = P*0.017097
P = 532/0.017097 = 31,116.45

This was the amount financed, so the original price is 3700 higher.
The cash price of the car was $31,116.45 +3,700 = $34,816.45