Question

A borrower is repaying a $19000 loan at 9.2%/year compounded monthly with monthly payments over 26 years. Just after the 78th payment he has the loan refinanced at 7.2%/year compounded monthly. If the number of payments remains unchanged, what will be the new monthly payment?

Answer 1

First we calculate present payment that borrower is paying.

Number of Monthly Installments = 26 * 12 = 312

Loan Amount or PV = 19,000

Yearly rate of interest = 9.2%

Monthly rate of interest = 9.2%/12 = 0.7667%

FV = 0

EMI value = Principal value * Rate of Interest * (1 + rate of interest)time / ((1+ rate of interest)time - 1))

EMI value = 19,000 * 9.2%/12 * (1 + 9.2%/12)312 / ((1+ 9.2%/12)312 - 1))

EMI Value = 1,578.45/ 9.84

EMI Value = 160.48

Total Payment after 78 periods = 78 * 160.48

Total Payment after 78 periods = 12,517.14

We will look at below image for interest component and principal component by end of 78 periods:

Principal paid = 1,573.03

Principal left = 19,000 - 1,573.03

Principal left = 17,426.97

New Interest Rate = 7.2%/12 = 0.6%

Number of payments left = 312 - 78

Number of payments left = 234

Payment = 17,426.97 * 7.2%/12 * (1 + 7.2%/12)234 / ((1+ 7.2%/12)234 - 1))

Payment = 138.79