You are considering borrowing $150,000 to purchase a new
home.
a. Calculate the monthly payment needed to amortize an 8
percent fixed-rate 30-year mortgage loan.
b. Calculate the monthly amortization payment if the loan in (a)
was for 15 years.
http://www.mortgagecalculator.org/
pmt = principal [ r/ {1 - (1+r)^-n} ]
here
principal = 150,000
r = interest rate / month = .08/12 =.006666666
n = 12 * 30 = 360 months
I get
1100.65 per month
that calculator link also says 1100.65
To calculate the monthly payment for the mortgage loan, we can use the formula for amortization:
Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)
where:
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate / 12)
n = Number of monthly payments (loan term in years * 12)
a. For a 30-year mortgage loan with an 8 percent fixed interest rate:
P = $150,000
r = 8% / 100 / 12 = 0.006666667
n = 30 * 12 = 360
Substituting the values into the formula:
Monthly Payment = $150,000 * 0.006666667 * (1 + 0.006666667)^360 / ((1 + 0.006666667)^360 - 1)
Using a calculator, the monthly payment for this loan would be approximately $1,100.65.
b. For a 15-year mortgage loan with an 8 percent fixed interest rate:
P = $150,000
r = 8% / 100 / 12 = 0.006666667
n = 15 * 12 = 180
Substituting the values into the formula:
Monthly Payment = $150,000 * 0.006666667 * (1 + 0.006666667)^180 / ((1 + 0.006666667)^180 - 1)
Using a calculator, the monthly payment for this loan would be approximately $1,432.86.
To calculate the monthly mortgage payment for a fixed-rate mortgage loan, you can use the formula for amortization. The formula is:
M = P * (r * (1+r)^n) / ((1+r)^n - 1)
Where:
M = Monthly payment
P = Principal loan amount (in this case, $150,000)
r = Monthly interest rate (annual interest rate divided by 12 and converted to decimal)
n = Number of payments (in this case, number of years multiplied by 12)
Let's calculate the answers to the given questions:
a. Calculate the monthly payment for a 30-year mortgage loan at an 8% interest rate:
Principal loan amount (P) = $150,000
Monthly interest rate (r) = 8% / 12 = 0.08 / 12 = 0.0067 (rounded)
Number of payments (n) = 30 years * 12 = 360
Using the formula: M = P * (r * (1+r)^n) / ((1+r)^n - 1)
M = 150,000 * (0.0067 * (1+0.0067)^360) / ((1+0.0067)^360 - 1)
M ≈ $1,101.75
Therefore, the monthly payment needed to amortize an $150,000 loan with an 8% interest rate over 30 years is approximately $1,101.75.
b. Calculate the monthly payment for a 15-year mortgage loan at an 8% interest rate:
Principal loan amount (P) = $150,000
Monthly interest rate (r) = 8% / 12 = 0.08 / 12 = 0.0067 (rounded)
Number of payments (n) = 15 years * 12 = 180
Using the formula: M = P * (r * (1+r)^n) / ((1+r)^n - 1)
M = 150,000 * (0.0067 * (1+0.0067)^180) / ((1+0.0067)^180 - 1)
M ≈ $1,269.91
Therefore, the monthly payment needed to amortize an $150,000 loan with an 8% interest rate over 15 years is approximately $1,269.91.