Question

Suppose you borrowed $10,000 at an interest rate of 12%, compounded monthly over 36 months. At the end of the first year (after 12 payments), you want to negotiate with the bank to pay off the remainder of the loan in 8 equal quarterly payments. What is the amount of this quarterly payment, if the interest rate and compounding frequency remain the same?

Please provide the answer showing all steps.

Answer 1

USING FINANCIAL CALCULATOR
Step 1:
Original Monthly payment
PV=-10000
I/Y=12%/12=1%
N=36
FV=0
CPT PMT=$332.14

Step 2:
Loan balance after 12 months
N=12
PMT=332.14
PV=-10000
I/Y=12%/12=1%
CPT FV=$7,055.84

Step 3:
Quarterly compounded rate
=((1+12%/12)^(12/4)-1)*4
=12.12%

Step 4:
New monthly payment
N=8
PV=-7055.84
FV=0
I/Y=12.12%/4
CPT PMT=$1,006.43