Find the monthly payment.
Mortgage amount Annual percentage rate
2. $146,800 5.25% 30 years
4. $113,400 5% 15 years
6. Find the interest paid the mortgage in exercise 2.
8. Find the total interest paid for the mortgage in exercise 4.
P = (Po*r*t)/(1-(1+r)^-t)
2. Po = $146,800
r = (5.25%/12)/100% = 0.004375 = Monthly
% rate.
t = 30yrs. * 12mo./yr. = 360 Months.
Plug the above values into the given Eq
and get: P = $291,828.61
Monthly Payment = P/t
4. Same procedure as #2.
6. I = P-Po
8. I = P-Po
To calculate the monthly payment for a mortgage, you can use the formula for calculating the monthly payment for a fixed-rate mortgage. The formula is:
P = (Pv * r) / (1 - (1 + r)^-n),
where:
P: Monthly payment
Pv: Present value (mortgage amount)
r: Monthly interest rate (annual percentage rate divided by 12)
n: Total number of monthly payments (number of years multiplied by 12)
Let's calculate the monthly payment for exercise 2:
1. Convert the annual interest rate to a monthly interest rate:
r = 5.25% / 100 / 12 = 0.004375.
2. Convert the number of years to the total number of monthly payments:
n = 30 years * 12 = 360.
3. Substitute the values into the formula:
P = (146,800 * 0.004375) / (1 - (1 + 0.004375)^-360).
P = $827.09.
Therefore, the monthly payment for exercise 2 is $827.09.
Now, let's calculate the monthly payment for exercise 4:
1. Convert the annual interest rate to a monthly interest rate:
r = 5% / 100 / 12 = 0.004167.
2. Convert the number of years to the total number of monthly payments:
n = 15 years * 12 = 180.
3. Substitute the values into the formula:
P = (113,400 * 0.004167) / (1 - (1 + 0.004167)^-180).
P = $894.73.
Therefore, the monthly payment for exercise 4 is $894.73.
To find the interest paid on a mortgage, you can calculate the total interest amount paid over the life of the mortgage.
For exercise 2:
1. Calculate the total payment over the life of the mortgage:
Total payments = Monthly payment * Total number of payments.
Total payments = $827.09 * 360.
Total payments = $297,752.40.
2. Calculate the total interest paid:
Total interest = Total payments - Mortgage amount.
Total interest = $297,752.40 - $146,800.
Total interest = $150,952.40.
Therefore, the interest paid for the mortgage in exercise 2 is $150,952.40.
For exercise 4:
1. Calculate the total payment over the life of the mortgage:
Total payments = Monthly payment * Total number of payments.
Total payments = $894.73 * 180.
Total payments = $160,851.40.
2. Calculate the total interest paid:
Total interest = Total payments - Mortgage amount.
Total interest = $160,851.40 - $113,400.
Total interest = $47,451.40.
Therefore, the total interest paid for the mortgage in exercise 4 is $47,451.40.