Question

A home was bought with a $400,000 mortgage. The interest rate was 4.4% and the term is 30 years (paid monthly). If they are selling the house at the end of year 8, what is the loan payoff amount? The monthly payment is $2,003.04 per month.

Answer #1

Given about a loan,

Loan amount = $400000

Interest rate r = 4.4% p.a. compounded monthly

Term in year = 30

As already calculated, monthly payment PMT = $2003.04

So, after 8 years, years remaining for the loan is 22 years

So, Loan payoff amount is amount that need to be paid at the end of year 8 sto clear off the debt.

So, loan payoff amount is PV of the remianing monthly payment

=> Loan payoff amount PV = PMT*(1 - (1+r/n)^(-n*t))/(r/n) = 2003.04*(1 - (1+0.044/12)^(-12*22))/(0.044/12) = $338414.51

So, Loan payoff amount is $338414.51

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