Question

TILip Submits Check my work 15 Daniel and Jan agreed to pay $556,000 for a four-bedroom colonial home in Waltham, Massachusetts, with a $70,000 down payment They have a 30-year mortgage at a fixed rate of 6.00 % 1 a. How much is their monthly payment? (Do not round intermediate calculations. Round your answer to the nearest cent.) points Monthly payment 2,913.82 eBook Print References b. After the first payment, what would be the balance of the principal? (Do not round intermediate calculations. Round your answers to the nearest cent.) Portion to Payment number Balance of loan outstanding Interest Principal 29,160.00 26,246.18 485,516.18

Answer 1

Answer a.

Price of Home = $556,000
Down Payment = $70,000

Amount Borrowed = Price of Home - Down Payment
Amount Borrowed = $556,000 - $70,000
Amount Borrowed = $486,000

Annual Interest Rate = 6.00%
Monthly Interest Rate = 0.50%

Period = 30 years or 360 months

Let Monthly Payment be $x

$486,000 = $x/1.005 + $x/1.005^2 + … + $x/1.005^359 + $x/1.005^360
$486,000 = $x * (1 - (1/1.005)^360) / 0.005
$486,000 = $x * 166.7916144
$x = $2,913.82

Monthly Payment = $2,913.82

Answer b.

First Payment:

Interest Paid = 0.50% * $486,000
Interest Paid = $2,430.00

Principal Repaid = $2,913.82 - $2,430.00
Principal Repaid = $483.82

Loan Outstanding = $486,000.00 - $483.82
Loan Outstanding = $485,516.18

Balance of Loan Portion to- Payment Number Outstanding 485,516.18 Principal 483.82 $ Interest 2,430.00 $