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?
i = .0525/12 = .004375
n = 12*15 = 180
P(1 - 1.004375^-180)/.004375 = 151000
solve for p
(a) Well, looks like the Fisher family found themselves a little fishy mortgage situation! To calculate their monthly payment, we'll need to dive into the ocean of mortgage formulas.
Let's start by finding out the loan amount. They bought the house for $191,000 and paid $40,000 down, so their loan amount is $191,000 - $40,000 = $151,000.
Next, we'll need to find the monthly interest rate. The annual interest rate is 5.25%, so the monthly interest rate would be 5.25% / 12 = 0.4375%.
Finally, we can use the good old mortgage payment formula: P = (r * A) / (1 - (1 + r)^(-n)), where P is the monthly payment, r is the monthly interest rate, A is the loan amount, and n is the number of payments.
Plugging in the values:
P = (0.4375% * $151,000) / (1 - (1 + 0.4375%)^(-15 years * 12 months)).
After doing the math, the Fisher family's monthly payment will be approximately $1,219.32. Let's hope they saved enough fish sticks for those monthly payments!
(b) Now let's calculate the total amount of interest they paid over the entire loan. We'll need to subtract the original loan amount from the total amount paid to find out the interest.
The total amount paid can be calculated by multiplying the monthly payment by the total number of payments. In this case, there are 15 years * 12 months = 180 total payments.
Total amount paid = $1,219.32 * 180 = $219,677.60.
Now, let's subtract the original loan amount from the total amount paid:
Total interest paid = $219,677.60 - $151,000 = $68,677.60.
So, the Fisher family paid approximately $68,677.60 in interest over the entire loan. That's enough to make even the clownfish frown!
To calculate the monthly payment and the total interest paid over the loan, we need to use the formula for calculating the monthly payment on a mortgage loan:
A = P * (r(1+r)^n) / ((1+r)^n - 1)
Where:
A = Monthly payment
P = Principal amount (remaining balance)
r = Monthly interest rate
n = Number of months
(a) to find the monthly payment, we need to find the principal amount first.
Principal amount = Total cost of the house - Down payment
= $191,000 - $40,000
= $151,000
(b) To find the monthly payment, we need to find the number of months first.
Number of months = Number of years * 12
= 15 * 12
= 180 months
Now we can substitute the values into the formula:
r = 5.25% / 100 / 12 (convert interest rate to decimal and monthly)
n = 180
Monthly payment = $151,000 * (0.004375(1.004375)^180) / ((1.004375)^180 - 1)
For simplicity in calculation, I will provide a rounded answer.
Monthly payment ≈ $1,200.20
(b) To find the total interest paid over the loan, we can subtract the principal amount from the total cost of the house:
Total interest paid = (Monthly payment * Number of months) - Principal amount
= ($1,200.20 * 180) - $151,000
Total interest paid ≈ $78,036
To find the monthly payment and the total interest paid on a mortgage, we can use the formula for calculating the monthly payment on a loan:
M = P [i(1 + i)^n] / [(1 + i)^n - 1]
Where:
M = Monthly payment
P = Loan amount (remaining balance)
i = Monthly interest rate
n = Total number of payments
Let's calculate the monthly payment first.
(a) Monthly Payment:
Loan amount (remaining balance) = Total house price - Down payment
P = $191,000 - $40,000 = $151,000
Monthly interest rate (i) = Annual interest rate / 12
i = 5.25% / 100 / 12 = 0.004375
Total number of payments (n) = Number of years * 12
n = 15 * 12 = 180
Substituting these values into the formula:
M = $151,000 [0.004375(1 + 0.004375)^180] / [(1 + 0.004375)^180 - 1]
M ≈ $1,218.18
Therefore, the Fisher family's monthly payment is approximately $1,218.18.
(b) Total Interest Paid:
Total interest paid = (Monthly payment * Number of payments) - Loan amount
Total interest paid = ($1,218.18 * 180) - $151,000
Total interest paid ≈ $117,672.40
Hence, the Fisher family paid approximately $117,672.40 in interest over the entire loan.