Question

Suppose you can afford to pay at most $2750 per month for a mortgage payment. If the maximum amortization period you can get is 15 years, and you must pay 3.5 What is the monthly interest rate corresponding to the effective annual rate? rm = What is the price of the most expensive house you can buy? What is the total interest paid?

Answer 1

To calculate the monthly interest rate corresponding to the effective annual rate, we first need to calculate the effective monthly rate using the formula:

1 + rm = (1 + re)^1/12

Where rm is the monthly interest rate and re is the effective annual rate.

Plugging in the values, we get:

1 + rm = (1 + 0.035)^1/12
1 + rm = (1.035)^(1/12)
1 + rm = 1.002881

Therefore, rm = 0.002881 or 0.2881%

Next, to calculate the price of the most expensive house you can buy, we use the formula for monthly mortgage payment:

P = C * (r/12) / (1 - (1 + r/12))^(-n*12)

Where P is the monthly payment, C is the loan amount, r is the monthly interest rate, and n is the number of years.

Plugging in the values, we get:

$2750 = C * (0.002881) / (1 - (1 + 0.002881))^(-15*12)
$2750 = 0.002881C / (1 - 0.9999624)
$2750 = 0.002881C / 0.0000376
C = $72,789.36

Therefore, the price of the most expensive house you can buy is $72,789.36.

To calculate the total interest paid, we use the formula for total interest paid on a mortgage:

Total Interest = (P * 12 * 15) - C

Plugging in the values, we get:

Total Interest = ($2750 * 12 * 15) - $72,789.36
Total Interest = $495,000 - $72,789.36
Total Interest = $422,210.64

Therefore, the total interest paid over the life of the mortgage is $422,210.64.