Question

You are looking to buy a car. You can afford $700 in monthly payments for five years. In addition to the loan, you can make a $800 down payment. If interest rates are 9.25 percent APR, what price of car can you afford (loan plus down payment)

Answer 1

$34,333

Step-by-step explanation:

A fix periodic payment for a specific period of time is an annuity payment. Price of the car can be determined by the sum of the present value of all payments and down payment made.

First we need o calculate the present value of annuity using following formula

Present value of annuity = P x [ 1 - ( 1 + r )^-n / r ]

P = periodic payment = $700

r = APR = 9.25 /12% = 0.77%

n = numbers of periods = 5 years x 12 months per year = 60 months

Placing values in the formula

Present value of annuity = $700 x [ 1 - ( 1 + 0.77% )^-60 / 0.77% ]

Present value of annuity = $33,532.88

Price of the car = Present value of annuity + Down Payment

Price of the car = $33,532.88 + $800 = $34,332.88