Question

Imagine you have $50,000 for a house down payment for a $250,000 home. Now, go through the process of estimating the monthly payments on a 30-year, fixed-rate mortgage of $200,000 assuming your mortgage carries a 5% interest rate. (Since we emphasized annual rather than monthly payments in this class, imagine you were paying your mortgage once a year and then divide by 12 months.) If you pay off the mortgage after thirty years, how much will you have paid in interest beyond the price of the house itself?

Answer 1

interest = 5% = 0.05

t = 30 yrs

Loan = 200000

Annual payment = 200000 * [0.05*((1 + 0.05)^30)/((1 + 0.05)^30-1)]

= 200000 * [0.05*((1.05)^30)/((1.05)^30-1)]

= 200000 * 0.035051435

= 13010.29

Since it is specifically mentioned the question to calculate monthly payments by dividing the annual payments by 12

Monthly payments = 13010.29 / 12 = 1084.19

Total amount paid in 30 yrs = 13010.29 * 30 = 390308.61

Total interest paid = total amount paid - total loan = 390308.61 - 200000 = 190308.61