Question

A homeowner takes out a 15-year mortgage in the amount of $400,000, fully amortized, monthly compounded, monthly payable, with an interest rate of 4.8% p.a. What is the remaining balance of the mortgage after 8 years (i.e., after the 96th payment)? (in %, 2 decimal places)

Answer 1

First calculate monthly payment:

P = Principal Loan =	$400,000.00
R = Rate or APR =	4.80%
N = Number of payments = 15*12 =	180
PMT = Payment = P x R/12 x (1+R/12)^N / ((1+R/12)^N - 1)
Payment =400000 x 4.8%/12 x (1+4.8%/12)^180 / ((1+4.8%/12)^180 -1) =	$3,121.6577

Finding outstanding balance at end of the particular time
P = Principal Loan =	$400,000.00
R = Rate or APR =	4.80%
n = Total number of payments done =	96
PMT =	3,121.65774
FV = Outstanding Balance = (P*(1+R/12)^n)-(PMT*((1+R/12)^n-1)/R/12)
FV = Outstanding Balance = (400000*(1+4.8%/12)^96)-(3121.65774*((1+4.8%/12)^96-1)/(4.8%/12) =	$    222,338.34