Question

You need a loan for your new house that you want to buy. The amount you borrow is $550,000 and the annual interest rate is 2% for 30 years. How much interest do you need to pay?

Answer 1

Answer:

Step-by-step explanation:

In the real world amortization mortgage loans have equal monthly installments paid for the life of the loan.

The monthly installments are found by

$I=P\left(\frac{r-1}{r^n-1}+(r-1)\right)\\ \\ r=1+(r/12),\ n=12(30)=360\\ \\ I=550000\left(\frac{.00167}{1.00167^{360}-1}+.00167\right)\\ \\ I=\ 2032.91\\ \\ \text{If we subtract the total paid over thirty years minus the principal we get the total interest paid.}\\ \\ 360(2032.91)-550000= 181846.56$