Taylor has a credit card with an interest rate of 24.5% compounded monthly that she must pay off in seven years. If her balance on the credit card is $2,345, what must her monthly payment be?

Question

amistre64 · Answer

m1 = B(1+r/12) - P
m2 = B(1+r/12)^2 - P(1+r/12) - P
m3 = B(1+r/12)^3 - P(1+r/12)^2 - P(1+r/12) - P

the balance looks to be an exponential deal, while the Payments follow a geometric series

amistre64 · Answer

since there are 7*12 periods to account for

$$M_n=B(1.r)^n-P~\frac{1-(1.r)^n}{1-1.r}$$
$$M_{84}=B(1.r)^{84}-P~\frac{1-(1.r)^{84}}{1-1.r}$$
$$0=B(1.r)^{84}-P~\frac{1-(1.r)^{84}}{1-1.r}$$
$$P~\frac{1-(1.r)^{84}}{1-1.r}=B(1.r)^{84}$$

$$P=B(1.r)^{84}\frac{1-1.r}{1-(1.r)^{84}}$$