The Fisher family bought a house for $191,000. They paid $40,000 down and took out a 15
year mortgage for the remaining balance at 5.25%, compounded monthly.
(a) What is their monthly payment?
(b) How much interest did they pay over the entire loan?
(a) To calculate the monthly payment, we first need to determine the remaining balance on the mortgage. Since they put $40,000 down, the remaining balance is:
$191,000 - $40,000 = $151,000
Next, we need to use the formula for the monthly payment on a mortgage:
M = P * (r/12) * (1 + r/12)^n / [(1 + r/12)^n - 1]
Where:
M = monthly payment
P = principal (remaining balance)
r = annual interest rate (5.25%)
n = number of payments (15 years * 12 months per year = 180 payments)
Plugging in the values, we get:
M = $151,000 * (0.0525/12) * (1 + 0.0525/12)^180 / [(1 + 0.0525/12)^180 - 1]
M = $1,214.73
Therefore, their monthly payment is $1,214.73.
(b) To calculate the total interest paid over the entire loan, we can use the formula:
Total interest = (monthly payment * number of payments) - principal
Plugging in the values, we get:
Total interest = ($1,214.73 * 180) - $151,000
Total interest = $219,451.40 - $151,000
Total interest = $68,451.40
Therefore, they paid $68,451.40 in interest over the entire loan.
To find the monthly payment, we will use the formula for the monthly payment on a mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = Monthly payment
P = Principal (loan amount)
i = Interest rate per period (monthly interest rate)
n = Total number of periods (number of months)
(a) Monthly Payment:
Principal (P) = $191,000 - $40,000 = $151,000
Interest Rate per period (i) = 5.25% / 100 / 12 = 0.004375
Total number of periods (n) = 15 years * 12 months/year = 180 months
Substituting these values into the formula:
M = $151,000 [ 0.004375(1 + 0.004375)^180 ] / [ (1 + 0.004375)^180 - 1 ]
Calculating this expression will give us the monthly payment for the Fisher family.
(b) To find the total interest paid over the entire loan, we will calculate the total amount paid over the loan term and then subtract the principal.
Total Amount Paid = Monthly Payment * Total Number of Payments
Interest Paid = Total Amount Paid - Principal
Let's calculate both values.
Please note that the results may vary slightly due to rounding.