Mortgage Loan

I had thought I understood how the calculation of mortgage payments actually worked; now I’m not quite so sure and had thought I would give a hypothetical scenario, so that I could resolve this issue.

This is how I thought calculating a mortgage payment would work. Let’s say hypothetically a home was $50,000 and I was required to put 10% down. That would mean the principle would be $45,000. Let’s say I had a 30 year mortgage.There’s 360 Months in 30 years, so I took 45,000 and divided it by 360 That would make my monthly payment $125.00 monthly. Let’s say the interest rate I had was 10%. 10% of 125.00 is 12.50, which would bring my monthly payment to $137.50.

Now I know my approach is flawed because when I use the online mortgage calculator it says a 45,000 principle with a 10% interest rate at a 30 year loan would give me a monthly payment of $394.91.

I’m just wondering what it is I’m doing incorrectly. Thanks in advance for your time.

You are basically saying the portion of each monthly payment going towards interest is the same for all 360 payments. The usual calculation assumes that each payment first covers the monthly interest on the principal, and then the remainder reduces the principal. Then the next payment also covers the monthly interest on the principal, but it is a lesser principal and therefore a lesser interest amount.

The online calculator uses this formula: A = P*(1-v^n)/i, where A is the original principal, P is the monthly payment, i is the monthly interest rate, v=1/(1+i), n is the number of monthly payments. In your example, 45000 = P*(1-1/(1+.10/12)^360)/(.10/12), from which P = 394.91