Question

An auto repair shop borrowed ​$18,000 to be repaid by monthly payments over 7 years. Interest on the loan is 6% compounded monthly.

​(a) What is the size of the periodic​ payment?

​(b) What is the outstanding principal after payment 31​?

​(c) What is the interest paid on payment 32​?

​(d) How much principal is repaid in payment 32​?

Answer 1

PV of loan amount =18000
Number of months =7*12 =84
Rate per month =6%/12 =0.5%
a) Size of Periodic Payment =PV/((1-(1+r)^-n)/r) =18000/((1-(1+0.5%)^-84)/0.5%) =262.9540 or 262.95

b)Outstanding Balance on Payment 31 =PV*(1+r)^n-PMT*((1+r)^n-1)/r) =18000*(1+0.5%)^31-262.954*((1+0.5%)^31-1)/0.5%)
=12216.17

c) Interest paid on payment 32 =12216.17*0.5% =61.08

d) Principal in rapid in payment 32 =Periodic Payment-Interest paid on payment 32 =262.95-61.08 =201.87