You have just taken a 30-year mortgage loan for $200,000. The annual percentage rate on the loan is 8%, and payments will be made monthly. Estimate your monthly payments.
Estimate ??
The standard simple formula and a good calculator gives you the answer in less than a minute.
i = .08/12 = .006666...
n = 30(12) = 360
P( 1 - 1.00666..^-360)/.00666.. = 200000
P = $ 1467.53
To estimate your monthly mortgage payments, we need to use a formula called the amortization formula. The formula is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where:
M = monthly payment
P = principal loan amount
i = monthly interest rate (annual interest rate divided by 12)
n = total number of months
Let's calculate the monthly mortgage payment for your $200,000 loan with an 8% annual percentage rate:
Step 1: Calculate the monthly interest rate
i = 8% / 12 = 0.00667
Step 2: Calculate the total number of months (30 years = 360 months)
n = 30 years * 12 months = 360 months
Step 3: Plug the values into the formula and solve for M
M = $200,000 [ 0.00667(1 + 0.00667)^360 ] / [ (1 + 0.00667)^360 – 1 ]
Using a calculator, you can simplify the equation and find your monthly mortgage payment. The estimated monthly payment for your 30-year, $200,000 mortgage with an 8% annual percentage rate should be around $1,467.53.