Question

You have decided to buy a house. You can get a mortgage rate of 5.5 percent, and you want your payments to be $1,175 or less. How much can you borrow on a 20-year fixed-rate mortgage? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

A homeowner takes out a $407,000, 30-year fixed-rate mortgage at a rate of 5.25 percent. What are the monthly mortgage payments? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer to Question 1:

Annual Interest Rate = 5.50%
Monthly Interest Rate = 0.4583%
Period = 20 years or 240 months
Monthly Payments = $1,175

Amount Borrowed = $1,175/1.004583 + $1,175/1.004583^2 + … + $1,175/1.004583^239 + $1,175/1.004583^240
Amount Borrowed = $1,175 * (1 - (1/1.004583)^240) / 0.004583
Amount Borrowed = $1,175 * 145.377423
Amount Borrowed = $170,818.47

Answer to Question 2:

Annual Interest Rate = 5.25%
Monthly Interest Rate = 0.4375%
Period = 30 years or 360 months
Amount Borrowed = $407,000

Let monthly payment be $x

$407,000 = $x/1.004375 + $x/1.004375^2 + … + $x/1.004375^359 + $x/1.004375^360
$407,000 = $x * (1 - (1/1.004375)^360) / 0.004375
$407,000 = $x * 181.092592
$x = $2,247.67

Monthly Payment = $2,247.67