You have a balance of $7500 on your credit card and you make no further charges. If

your APR is 12.5% and each month you make only the minimum payment of 5% of
your balance, then find a formula for the balance after
t
monthly payments.

A) 7500(0.959896)
t
B) 7500(0.940104)
t
C) 7500(1.03906)
t
D) 7500(1.06094)
t

1 answer

i = .125/12 = .01041666..

balance after 1 month before payment
= 7500(1.01041666.)
payment = .05 of balance
balance at end of month 1 = 7500(.95)(1.0104166)

balance after month 2 before payment
= 7500(.95)(1.0104166)^2
payment = .05 of that balance
balance at end of month 2
= 7500(.95)^2 (1.0104166)^2
= 7500(.9598958..)^2

balance at end of month t
= 7500(.9598958..)^t

the closest would be A) if it had been typed correctly