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
`(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=(r(PV))/(1-(1+r)^(-n))`.

Rearranging the above equation,

`P[1-(1+r)^(-n)]=r(PV)\\ </p><p>P-r(PV)=P(1+r)^(-n)\\ </p><p>(P-r(PV))/(P)=(1+r)^(-n)\\ </p><p>n=(\ln ((P)/(P-r(PV)) ))/(\ln(1+r)) </p><p>`

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

`n=(\ln ((152.5)/(152.5-0.0107(2200)) ))/(\ln(1+0.0107))=15.75`.

Crissy has to make
`16` loan payments.