The Important Math of Mortgage Payment

You want to buy a home for 500 thousand dollars and you'll make a down
payment of 100 thousand dollars. The interest rate is 6.7% for 30 years'
mortgage. What would be your monthly mortgage payment?

For questions like this, remember this useful formula:
Say, 'L' is your loan amount (in this example 500-100 = 400 thousand)
Say, 'i' is your annual interest rate (here, 0.067)
Say, N = No. of months = 30 X 12 = 360

Then calculate the following steps:
- Calculate (1+i/12) = (1+0.067/12) = 1.0056
- Raise this number to the power of N = 1.0056^360 = 7.4217 = X (say)
- Calculate (1 - 1/X) = 0.8653 = Y (say)
- Calculate L*i/12 = 400000*0.067/12 = 2233.33 = Z (say)
- Divide Z by Y = 2581.11

So, your monthly mortgage payment is 2581.11$.
You may try another exercise: What would be your monthly payment if
your interest rate is 6.0 % for a 15 years' mortgage? [Ans. $3375.43]