Question

Mary takes out a 25-year mortgage of $280,000, to be repaid with monthly payments, the first coming a month from now. If the annual interest rate is 8.8% compounded monthly, what is the total amount of interest that she’ll pay over the life of the loan, rounded to the nearest dollar?

Answer 1

Given total mortgage of $280,000 (P)

No of installments to be paid= (25years*12 months)-300 installments(n)

Interest= 8.8% compunded monthy so monthly interest- 8.8%/12=0.73%(r)

Formula to calculate equated monthly payments=

P*r*(1+r)^n/((1+r)^n-1)

=280000*.73%(1+.73%)^300/((1+.73%)^300-1)

By using excel or calculator we can find (1.0073)^300=8.9528

= 2053.33(8.9528)/(8.9528-1)

=2311.522

So we need to pay monthly 2311.522$

so for 300 installments we need to pay 2311.522$*300=693456.5$

Total repayment amount= total Principal paid +total interest paid

693456.5$=$280,000+ interest paid

=Total interest paid= 693456.5$-$280,000=$413456.45