Question

15 43 A buyer purchases a home for $4,500,000. They have acquired a 30-year loan at 6.5% interest with a 20% downpayment. Which of the following is the amount of interest that the buyer needs to pay over the life of the loan? A) $4,591,601.60 B) $4,321,125.30 C) $4,186,475.50 D) $2,134,925.10

Answer 1

Answer is $4,591,601.60

Cost of home = $4,500,000

Down payment = 20% * Cost of home
Down payment = 20% * $4,500,000
Down payment = $900,000

Amount borrowed = Cost of home - Down payment
Amount borrowed = $4,500,000 - $900,000
Amount borrowed = $3,600,000

Annual interest rate = 6.50%
Monthly interest rate = 0.54167%

Time period = 30 years or 360 months

Monthly payment be $x

$3,600,000 = $x/1.0054167 + $x/1.0054167^2 + $x/1.0054167^3 + .... + $x/1.0054167^360
$3,600,000 = $x * (1 - (1/1.0054167)^360) / 0.0054167
$3,600,000 = $x * 158.210161
$x = $22,754.45

Monthly payment = $22,754.45

Total amount paid = 360 * $22,754.45
Total amount paid = $8,191,601.60

Total interest paid = Total amount paid - Amount borrowed
Total interest paid = $8,191,601.60 - $3,600,000.00
Total interest paid = $4,591,601.60