Question

You have $4,500 on a credit card that charges a 21% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)? S each month Submit Question

Answer 1

We can use the present value of the annuity formula:

$\small \textup{PVA} = \textup{A}\left [\frac{(1-(1+i/a)^{-na})}{i/a} \right ]$

Where,
PVA = Present value of the annuity
A = Monthly payment
i = Interest rate in decimal form (i.e 21% = 0.21)
n = Number of years
a = Number of payments in a year

Therefore,

$\small \textup{4500} = \textup{A}\left [\frac{(1-(1+0.21/12)^{-5*12})}{0.21/12} \right ]$

$\small \textup{4500} = \textup{A}\left [\frac{(1-(1.0175)^{-60})}{0.0175} \right ]$

$\small \textup{4500} = \textup{A}\left [\frac{1-0.35313}{0.0175} \right ]$

$\small \textup{4500} = \textup{A}\left [\frac{0.64687}{0.0175} \right ]$

$\small \textup{4500} = \textup{A}(36.964)$

$\small A = \frac{\textup{4500}}{36.964}$

$\small = \$121.74$

Therefore, you have to pay $121.74 each month.

Excel formulas:

A B с 1 Credit card balance 4500 2 Interest 21% 3 Number of years 5 4 Monthly payment $121.74 5 Formula for monthly payment |--PMT(B2/12,B3*12,B1) 6