Question

Brenda has taken out a $1300 loan to pay for a hot tub. She will make monthly payments for a year at an interest rate of 10 %, compounded monthly.

How much interest will she end up paying?
Select one:
a. $213.45
b. $71.49
c. $112.56
d. $110.89
What i don't understand is what amount is the monthly payment?

Answer 1

The monthly payment A over N=1 year(s) for a loan P=1300 at a nominal annual interest rate of i=0.10, compounded c=12 times annually is given by

To simplify the formula, we write
n=c*N=12*1=12=number of periods
R=1+i/c=1+0.1/12=interest rate per period
then monthly payment, A
<b>A=P((R-1)R^n)/(R^n-1)</b>
=1300(.0083333(1.0083333^12)/(1.0083333^12-1)
=114.2907 for 12 months.

The interest she ends up paying is 12 times the amount, less the 1300 that she borrowed.