Question

The outstanding balance on Bill's credit card account is 3690 dollars. The bank issuing the credit card is charging 21 percent of interest per year compounded monthly. If Bill decides to pay off his balance in equal monthly installments at the end of each month for the next 17 months, how much will be his monthly payment?

Answer 1

Use the compound interest formula:
P=$3690
i=0.21/12=0.0175
n=17
M=amount of monthly payment

Amount after 17 months (without payment)
= A(1+i)^n

Value of his payments at the same interest rate
=M+M(1+i)+M(1+i)^2+...+M(1+i)^(n-1)
=M((1+i)^n-1)/(1+i-1)
=M(1+i)^n/i

Equate the two:
M((1+i)^n-1)/i = A(1+i)^n
=>
M=A(1+i)^n*i/((1+i)^n-1)
=3690(1.0175)^17*0.0175/(1.0175^17-1)
=$252.824

Answer 2

Correction in an intermediate step (only):
...
=M((1+i)^n-1)/(1+i-1)
=M((1+i)^n-1)/i