Question

Karl owes $7,464 on a credit card with a 20.4% interest rate compounded monthly. What is the monthly payment he should make in order to pay off this debt in 12 months, assuming he does not charge any more purchases with the card?

$692.85

$1,706.57

$139.17

$622.00

Answer 1

What do you know of basic principles? This will solve ALL such problems.

i = 0.204 -- Annual interest rate to be compounded monthly
j = i/12 = 0.017 -- Monthly interest rate
r = 1+j = 1.017 -- Monthly interest accumulation factor.
Pmt is the amount of the monthly payment,
That's all we need - along with a little algebra.

After one month
(7464*r - Pmt)
After two months
((7464*r - Pmt)*r - Pmt)
After three months
(((7464*r - Pmt)*r - Pmt)*r - Pmt)
...
After 12 months
Long tired expression = 0

After a little algebra
7464r^12 - Pmt*r^11 + Pmt*r^10 + ... + Pmt = 0

More algebra
7464r^12 - Pmt*(r^11 + r^10 + ... + r^0) = 0

Your challenge is to add up what is in those parentheses.