Question

You have just purchased a home and taken out a $275,000 mortgage. The mortgage has a 25-year term with monthly payments and an APR of 3% compounding monthly. How much of your 288th payment will be interest and how much will go toward reducing your principal?

Answer 1

Monthly Payment = {Present value * Interest rate} / [1-(1+interest rate)^{-number of periods}]

Payment = {275000 * [3%/12]} / [1-(1+3%/12)^-25*12]

Payment =(275000*0.0025) / [1- (1+0.0025)^-300]

Payment =687.5/ [1- (1.0025)^-300]

Payment =687.5/ [1- 1/(1.0025)³⁰⁰]

Payment =687.5/ [1- 1/2.11502]

Payment =687.5 / 0.52719

Payment = 1304.08

Calculation of Monthly interest payment :

Monthly payment = 1304.08

less : Monthly Principal payment [275000/300] = 916.67

Monthly Interest payment = 387.41

Interest of 288th payment = 387.41

Principal of 288th payment = 916.67

Note:- 1) Total amount of interest upto 288th payment = 288* $387.41 = $111574.08

2) Total amount of principal upto 288th payment = 288* $916.67 = $264000.96