Question

You just bought a house and borrowed 15-year mortgage at 5% APR, compounded monthly. Your loan amount is $250,000.

1. Calculate your monthly payment

2. Calculate the principal and interest portions of your 1st and last payment

3. Calculate how much principal and interest you paid within 5 years and your outstanding balance at the end of the fifth year.

Answer 1

Amount borrowed (PV) = -$250,000

Number of monthly installments to be paid (N) = 15*12 = 180

Monthly interest rate (I) = 5%/12 =0.4167%

monthly payment (PMT) = ??

Using financial calculator or PMT function in excel,

Monthly payment (PMT) = $ 1,976.98

Interest portion for 1st installment = 250,000 x 0.4167% = $ 1041.67

Therefore Principal portion for 1st installment = $ 1976.98 - $ 1041.67 = $ 935.32

Interest portion for last installment = 1976.98 / (1+0.4167%) x 0.4167% = $8.20

Therefore Principal portion for 1st installment = $ 1976.98 - $ 8.20 = $ 1968.78

Outstanding balance at the end of year 5

Monthly payment (PMT) = $ 1,976.98
Number of pending monthly installments to be paid (N) = 10*12 = 120

Monthly interest rate (I) = 5%/12 =0.4167%

Balance at the end of year 5 (PV) =??

Using financial calculator or PMT function in excel,

Balance at the end of year 5 (PV) =186,392.73

Principal paid in 5 years = $250,000 - $186,392.73 = $ 63,607.27

Total amount paid in 5 years = 1976.98 x 5 x 12 = $ 118,619.04

Therefore interest paid in 5 years = total payment - principal payment = 118619.04 - 63607.27 = $ 55,011.77