You have a $4473 credit card debt, and you plan to pay it off through monthly payments of $76. If you are being charged 18% interest per year, how long (to the nearest tenth of a year) will it take you to repay your debt?

Question

anonymous · Answer

Hmmmmm, I'm sure there is a formula, but I don't remember it...

anonymous · Answer

i have multiple choices answers lol

anonymous · Answer

I'd consider it like a series... $$
a_0 = 4473 \
a_1 = [a_0-12(76)](1+0.18)\
a_n = 1.18a_{n-1}-1.18(12)(76)
$$

anonymous · Answer

im just tryin to up some extra credit.. but im pretty sure im going to still end up failing the course :(

anonymous · Answer

$$
a_n = 1.18[1.118a_{n-2}+1.18(12)(76)]+1.18(12)(76)
$$

anonymous · Answer

$$
a_n = (1.18)^2a_{n-2}+(1.18)^2(12)(76) + (1.18)(12)(76)
$$

anonymous · Answer

$$
a_n = (1.18)^na_0+(12)(76)\sum_{k=1}^n(1.18)^k
$$

anonymous · Answer

Hmmmm, interesting... a geometric series...

anonymous · Answer

Suppose $P_0=a_0, r=0.18,m=76$:$$
P(t) = (1+r)^t+\frac{12m}{1+r}\sum_{k=0}^{t-1}(1+r)^k=(1+r)^t+\frac{12m}{1+r} \frac{1-(1+r)^{t-1}}{1-(1+r)}
$$

This would be a lot easier if you gave me whatever formula you were given...