Question

A borrower has a $50000 loan with the "Easy-Credit" Finance Company. The loan is to be repaid over 14 years via monthly payments at 8.6%/year compounded monthly. Just after the 7th payment, the borrower learns that his local bank would lend him money at 6.6%/year compounded monthly. Assuming that the contract stipulates an early repayment penalty equal to the interest rate differential times the outstanding balance times the term remaining in the standard 5-year guaranteed interest period, what would be the new monthly payment?

Answer 1

Monthly payments of original loan= $512.84 calculated as follows:

Principal outstanding after 7th payment =   $ 48,894.89    Calculated as the PV of remaining (unpaid ) monthly installments as an annuity follows:

It is assumed that the remaining term for the purpose of calculation penalty is the remaining number of months (in terms of years) of the initial 5 year period.

Hence remaining term for penalty=(12*5)-7 = 53/12

Penalty for prepayment= Loan balance*Interest differential*Remaining period

= $ 48,894.89 * (8.6-6.6)% *53/12 = $ 48,894.89*2%*53/12 = $4,319.05

New Loan amount= Balance + Penalty = $ 48,894.89+ $4,319.05 = $53,213.94

New monthly payment= $ 499.03 as follows: