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

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