Question

You are looking to buy a car. You can afford $380 in monthly payments for four years. In addition to the loan, you can make a $1,700 down payment. If interest rates are 8.75% APR, what price of the car can you afford (loan plus down payment)?

a) $17,049.67
b) $18,596.82
c) $20,745.31
d) $22,895.11

Answer 1

If you are looking to buy a car. You can afford $380 in monthly payments for four years. The price of the car that you can afford (loan plus down payment) is:a) $17,049.67.

What is the price?

To determine the price of the car you can afford (loan plus down payment) use the present value formula for an installment loan. The formula is:

PV= PMT×(1−(1+r)^ −nt )​ −DP/r

Where:

PV= present value (total price of the car),

PMT= monthly payment,

r monthly interest rate (APR divided by 12),

n total number of payments (number of months),

t = time in years, and

DP = down payment.

So,

PMT = $380

r=0.0875/12 (monthly interest rate)

n=4×12 (four years converted to months)

t=4 years

DP = $1,700

Plug in these values and solve for

`PV= 380* 1-(1+ 0. 0875/12) ^-4*12 ) -1700/0. 0875/12`

PV≈17,049.67

Therefore the correct option is a) $17,049.67.