Question

Jared can afford to make monthly payments of $360 for the nest 48 months. If his bank charges annual interest rates of 10% approximately how much money can Jared afford to borrow from his bank to buy the car?

Note: Please enter the answer rounded to the nearest dollar?

Answer 1

Here, the payments will be same every month, so it is an annuity. We need to calculate present value of annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $360, r is the rate of interest = 10%. Monthly rate = 10% / 12 = 0.83333% and n is the time period = 48 months

Now, putting these values in the above formula, we get,

PVA = $360 * (1 - (1 + 0.8333%)-48 / 0.8333%)

PVA = $360 * (1 - ( 1+ 0.008333)-48 / 0.008333)

PVA = $360 * (1 - ( 1.008333)-15 / 0.008333)

PVA = $360 * (1 - 0.67143210577) / 0.008333)

PVA = $360 * (0.32856789423 / 0.008333)

PVA = $360 * 39.4283050

PVA = $14194.19

So, he can afford to borrow $14194.19