Question

Crissy took out a loan for $2200 at a 16.8% APR, compounded monthly, to buy a laser printer. If she will make monthly payments of $152.50 to pay off the loan, how many total payments will she have to make? Show your work.

Answer 1

The answer is 17 for APEX

Answer 2

The monthly interest rate is $\frac{12.8}{12} =1.07\%=0.0.0107$.

The payment rate $P$, monthly interest rate $r$, present value $PV$ and the number of

periods are related as,

$P=\frac{r(PV)}{1-(1+r)^{-n}}$.

Rearranging the above equation,

$P[1-(1+r)^{-n}]=r(PV)\\ P-r(PV)=P(1+r)^{-n}\\ \frac{P-r(PV)}{P}=(1+r)^{-n}\\ n=\frac{\ln (\frac{P}{P-r(PV)} )}{\ln(1+r)}$

When $PV= 2200,r=0.0107,P= 152.5$,

$n=\frac{\ln (\frac{152.5}{152.5-0.0107(2200)} )}{\ln(1+0.0107)}=15.75$.

Crissy has to make $16$ loan payments.