I was looking at a debt and it laid out my how my payment went towards the debt. One column said "Payment Applied to Principal" and "Payment Applied to Interest." What does "applied to interest mean?" I once worked out the formula for paying off debt with compound interest. So, I have a general idea... Say I make a payment of x dollars. Then x-i is the payment applied to the principle while i is payment paid to interest. This i is defined be the amount of money that, if applied to the debt and then interest is compounded this, then the resulting new debt balance is exactly the same. Am I correct?
I believe you are correct, I'm understanding you correctly - i should be equal to the interest accrued during the payment period.
Or that... I just went too complicated. I really wanted to start defining functions and variables... but didn't Please Register or Log in to view the hidden image!
Compound interest is not involved. The following is a simple example. $716.43 is the monthly payment required to pay off a $100,000 in 20 years at 6% per year. The first month, InterestAmount = $500.00 & PrincipalAmount = $216.43, reducing the balance owed to $99,783.57 Second month: InterestAmount = $498.92 & PrincipalAmount = $217.51, reducing the balance owed to $99,566.06 Note that InterestAmount = .005 times the amount owed at the beginning of each month. There is a formula for calculating a level payment. There are tables published to allow the payment to be determined without using the formula. My HP50G calculator gave me the above payment amount. I have long since forgotten the formula & do not have tables readily available.
I think, with a fixed interest rate, you know exactly how much you have to pay back over your 20 year mortgage, for example. So when you make the loan, the interest is already computed, and you already owe $100,000 + 20 years of interest. This is why, for example, big loans have a penalty for paying them off early.
BenTheMan: The following is absolutely wrong unless you are not dealing with a legitimate bank or insurance company. The above type of interest repayment is called "Add-On" calculated interest & is often used by furniture stores or loan sharks. Considering a loan of $100,000 at 6% per year for 20 years, the above would result in $120,000 in interest & 100,000 for the principle repayment, or $220,000.00 as the total amount payed. The amount paid for a normally calculated 20 year mortgage is approximately $171,943.20 of which 71,943.20 is interest. $120,000 would be the total amount of interest if you paid nothing back until you paid off the entire loan after 20 years. It would also be the amount of interest paid if you paid only $500.00 each month for 20 Years (interest only, no payment toward principle). Note that when you make monthly payments of more than $500.00 per month, you do not have the entire $100,000 for 20 years.
It's just the bank's attempt to devise terminology that laymen will understand. (Or, perhaps, not understand, if you doubt the integrity of the banking system.) They're trying to come up with a parallel construction. You know what "applied to principal" means, so they are looking for words you'll understand, to tell you that the rest of your payment went to pay off the current billing cycle's interest. Compound interest generally does not come into play with debt management, only investments. When you loan money to a bank (i.e. open a savings account), you're generally expecting the bank not to start paying off that loan anytime soon. You're going to leave your money there for a long time, earning interest. The concept of compound interest is necessary for you to know how often your accrued interest is actually credited to your account, so that your balance increases, so that the next interest accrual will be calculated against a higher balance than the first one. If you invest $100 at 10% interest in a bank that only pays simple interest, using the most elementary definition of the term, they will pay you $10 interest on your original $100 every year, and at the end of the ten years you'll have $200. If the bank pays compound interest, compounded annually, at the end of the ten years you'll have around $260. If it's compounded quarterly, your payoff will be closer to $270, etc. Back in the 1970s (I think it was), banks offered the gimmick of interest compounding daily. Obviously this isn't going to make a significant difference in anybody's payoff; I'm too lazy to do the arithmetic but I doubt that your hundred bucks would even hit $280. Compounding is not an important concept in loan management. The bank accrues the interest every month and every month you make a payment. Your balance is recalculated for you so you never have to ask what figure the interest was computed from. If they were writing you a thirty-year mortgage with no monthly payments, but instead a balloon payment at the end of the term, then of course you'd be very interested to know how they were compounding the interest. If you have a $100K mortgage at 5% and they're only charging simple interest, then at the end of the 30 years you'd owe them $250K. But if they compound the interest annually, you'll owe $432K.
