A. To calculate the monthly payment, we can use the formula for a fixed-rate mortgage:
P = L[c(1 + c)^n]/[(1 + c)^n - 1]
Where:
P = Monthly payment
L = Loan amount (or mortgage amount)
c = Monthly interest rate (which is the annual interest rate divided by 12)
n = Total number of monthly payments (which is the number of years multiplied by 12)
Using the given values, we can calculate the monthly payment as follows:
c = 0.08/12 = 0.0066667 (monthly interest rate)
n = 30 x 12 = 360 (total number of monthly payments)
P = 450000[0.0066667(1 + 0.0066667)^360]/[(1 + 0.0066667)^360 - 1] = $3,284.62
Therefore, the monthly payment is $3,284.62.
B. After 2 years, we have made 24 monthly payments. To calculate the amount owed after 2 years, we can use the following formula:
A = L[(1 + c)^n - (1 + c)^p]/[(1 + c)^n - 1]
Where:
A = Amount owed after p periods (in this case, 2 years or 24 months)
L, c, and n are the same as in part A.
Using the given values, we can calculate the amount owed after 2 years as follows:
A = 450000[(1 + 0.0066667)^360 - (1 + 0.0066667)^24]/[(1 + 0.0066667)^360 - 1] = $438,499.34
Therefore, the amount owed after 2 years is $438,499.34.
C. To calculate the amount of interest paid over a 2-year period, we can subtract the amount of principal paid from the total payments made during that time. The total payments made over 2 years would be the monthly payment multiplied by the number of payments, which is 24 in this case:
Total payments = 24 x $3,284.62 = $78,830.88
To calculate the amount of principal paid, we can use an amortization table or a mortgage calculator. The amount of principal paid after 2 years is approximately $20,742.26.
Therefore, the amount of interest paid over a 2-year period is:
$78,830.88 - $20,742.26 = $58,088.62
Therefore, the amount of interest paid over a 2-year period is $58,088.62.
D. To calculate the monthly payment for a 20-year and a 15-year mortgage at the current rate of 3.75%, we can use the same formula as in part A, but with the new interest rate and term.
For a 20-year mortgage:
c = 0.0375/12 = 0.003125 (monthly interest rate)
n = 20 x 12 = 240 (total number of monthly payments)
P = 438499.34[0.003125(1 + 0.003125)^240]/[(1 + 0.003125)^240 - 1] = $2,596.47
Therefore, the monthly payment for a 20-year mortgage at 3.75% interest would be $2,596.47.
For a 15-year mortgage:
c = 0.0375/12 = 0.003125 (monthly interest rate)
n = 15 x 12 = 180 (total number of monthly