Question

For a standard, fully amortizing mortgage loan of $250,000, at 3.5 percent interest for 30 years, find the balance at the end of 5 years. If the borrower refinances the loan, how much would need to be refinanced at the end of 20 years?

Answer 1

Given that,

Loan amount = $250000

interest rate = 3.5% compounded monthly

term period = 30 years

So, monthly payment of the loan is calculated using annuity formula:

PMT = PV*(r/n)/(1 - (1+r/n)^(-n*t)) = 250000*(0.035/12)/(1 - (1+ 0.035/12)^(-12*30)) = $1122.61

So, after 5 years, period remaining of the loan = 25 years

So loan balance after 5 years is equal to PV of annuity for remaining 25 years

So, Loan remaining = PMT*(1 - (1+r/n)^(-n*t))/(r/n) = 1122.61*(1 - (1 + 0.035/12)^(12*25))/(0.035/12) = $224242.68

balance at the end of 5 years = $224242.68

So, at the end of 20 years, loan balance = = 1122.61*(1 - (1 + 0.035/12)^(12*10))/(0.035/12) = $113526

So, $113526 would be needed to refinanced the loan at the end of year 20