[Allen Farber]

Now if you're just going to call me an idiot or a child because I don't know this in the comment section, then don't bother replying. So initially, I thought that the simple interest formula was (Principal x Rate x Time) but someone told me I'm wrong without any explanation as to why I am. So if someone could please tell me the actual formula to figuring out how much interest I would owe for taking out a loan, please do so in the comment section.

DISCLAIMER: By the way, this loan scenario is an EXAMPLE and NOT A REAL SCENARIO for those of you who can't tell.

[ebaines]

It depends on the terms of the loan. If you borrow an amount of money and pay the loan off with a single payment then you would be correct - the interest amount would be the interest rate times the loan amount times the period of the loan. But most loans such as car loans or home mortgages involve multiple payments over time. For these types of loans it's not as simple as you thought because as you make loan payments a portion of your payment is the interest payment and a portion of the payment goes to paying down the outstanding principal amount. Over time as the principal balance declines you owe less interest each month, so more of your payment goes to paying in the principal.

The formula for the monthly payment amount is:



Where r = interest rate per payment perod, A= the loan amount, and n = the number of payments to be made. The total amount of interest paid over the life of the loan is equal to your total payments minus the initial principal amount:



For example, for a 30-year $100,000 mortgage at 5% interest per year, with monthly payments you have:

n = 30 years x 12 months/yr = 360
r = .05/12 = 0.0042/month
A = $100,000

and P turns out to be $536.82/month. Total payments over the life of the 30-year loan would be $536.42/month x 360 months = $193,256, and total interest paid would be $193,256 - $100,000 = $93,256.

Hope this helps.

[Allen Farber]

It deends on the terms of the loan. If you borrow an amount of money and pay the loan off with a single payment then you would be correct - the interest amount would be the interest rate times the loan amount times the period of the loan. But most loans such as car loans or home mortgages involve multiple payments over time. For these types of loans it's not as simple as you thought because as you make loan payments a portion of your payment is the interest payment and a portion of the payment goes to paying down the outstanding principal amount. Over time as the principal balance declines you owe less interest each month, so more of your payment goes to paying in the principal.

The formula for the monthly payment amount is:



Where r = interest rate per payment perod, A= the loan amount, and n = the number of payments to be made. The total amount of interest paid over the life of the loan is equal to your total payments minus the initial principal amount:



For example, for a 30-year $100,000 mortgage at 5% interest per year, with monthly payments you have:

n = 30 years x 12 months/yr = 360
r = .05/12 = 0.0042/month
A = $100,000

and P turns out to be $536.82/month. Total payments over the life of the 30-year loan would be $536.42/month x 360 months = $193,256, and total interest paid would be $193,256 - $100,000 = $93,256.

Hope this helps.

Thanks so much. Also, I don't expect you to know this but I'll ask anyway, would you happen to know the significance of the numbers and variables in the equation. The only part of your answer I'm confused on is how the equation gives the amount of money you owe. Specifically, the pair of "1" and the exponent. And if I paid more that I was supposed to do on a payment, would that go towards the principal?

[ebaines]

The derivation of the formula is a bit complicated - you can see it here: A Derivation of Amortization

Regarding paying more than the standard monthly payment - yes, the excess goes to paying off principal. This can be a very effective way to save significant amount of interest payments over the years.

[Allen Farber]

The derivation of the formula is a bit complicated - you can see it here: A Derivation of Amortization

Regarding paying more than the standard monthly payment - yes, the excess goes to paying off principal. This can be a very effective way to save significant amount of interest payments over the years.

Thanks, you explained to me in a few minutes what 2 hours of college banking courses couldn't explain to me