Question

If you use your credit card to purchase a leather jacket for $500 and only make the minimum payments of $25 a month, how long will it take you pay off the jacket at an annual percentage rate of 11.3% and how much will the jacket cost you in the end?

Answer 1

Here, the payments will be same every month, so it is an annuity. For calculating the number of months, we will use the present value of annuity formula as below:

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

where, PVA = Present value of annuity = $500, P is the periodical amount = $25, r is the rate of interest = 11.3%, so monthly rate = 11.3% / 12 = 0.941667% and n is the time period

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

$500 = $25 * (1 - (1 + 0.941667%)-n / 0.941667%)

$500 / $25 = (1 - ( 1+ 0.00941667)-n / 0.00941667)

20 = (1 - ( 1.00941667)-n / 0.00941667)

20 * 0.00941667 = (1 - (1.00941667)-n

0.1883333 = 1 - (1.00941667)-n

(1.00941667)-n = 1 - 0.1883333

(1.00941667)-n = 0.816667

(1.00941668)-n = (1.00941667)-21.6

n = 21.6

So, it will take 21.6 months.

Jacket cost = Monthly payments * Time period needed

Jacket cost = 21.6 * $25 = $540