It will be easier to understand if you treat interest the following way: it's the sum you pay the bank to get permission to not return the whole principal right now. You can then "goal seek" to find a payment, or a rate, that will pay off a particular balance in a set number of payments. Plugging this basic series of operations into rows of a spreadsheet allows you to count the number of payments by simply watching for when the balance drops below zero (you can easily set most spreadsheets up to subtract the lesser of the payment amount or the current balance plus interest, in which case when the balance and interest is less than the scheduled payment it will drop to zero and stay there). This is very easy to understand take your balance, add the amount of interest accrued each month based on the rate (1/12 of the APR), then subtract your scheduled payment, and the result is your new balance, on which you repeat the process the next month. You can also play "what-ifs" using what's called an "amortization table". The equation to calculate a periodic payment P for a loan of balance B at a periodic compounding rate R over a number of periods T is known as the "reverse annuity formula" (because it basically works the same for the bank as it would for you if you had the same balance B in a retirement account, earning R each period, and needed to take out P each period for T periods) and is as follows: The math behind this has been a staple of the financial industry for decades. As the remainder of your payment begins to whittle away at the principal amount, the accrued interest decreases, meaning that the same payment can now pay more principal, which further decreases the interest accrued on the lower balance, and so on. At the beginning of the loan, the balance is large and therefore so is the interest accrued each month. On top of this, you will want to pay some additional money to reduce the principal, otherwise you're paying interest forever (this is basically what large companies do by issuing coupon bonds, but I digress). They want their cost of capital that's why they gave you the loan in the first place. (Canadian Banks - Fixed Rate)īanks make you pay accrued interest on the current outstanding balance of the loan each month. In reality, the interest is calculated on the opening balance every six months. As the balance is (should be!) decreasing, so will the interest portion of the payment. In essence, the interest portion of the mortgage payment is the cost of borrowing the outstanding balance for 1 month. Nearer the end of the loan, when you have only 10,000 remaining, the interest portion will be nearer $100 a month, meaning you're paying principle much faster. On month three, we want to borrow $98,997.50 for a month at a cost of $494.99. What does it cost you to borrow this amount for one month? $497.5 - Leaving $502.50 towards principal. Now forget about the past, forget about the future. When you make your payment, $500 goes to interest, and 500 goes to principal. So, for the first month, it will cost you $500 in interest to borrow the entire balance for one month. This is a simplification, but it will illustrate the point.īorrow $100,000 at. That means the amount of principal paid must increase as you go along.Īssume a month to month mortgage. The standard amortization requires a fixed payment each month, but the interest amount still has to decline as the principal declines. Sixteen years after I took out a mortgage with a $1300/month payment, I find it fairly easy to pay, although it was a bit challenging to our cash flow initially. So, the amount of interest you pay each month declines, as does your monthly payment.īut for most people, paying big payments at the beginning and smaller ones toward the end is completely backwards, since most of us earn more as we progress in our careers. And so on, until the last month you will be paying $1010. The second month, the interest will be on $119K, so your payment will be $2190. So what's the interest for month 1? One percent of $120K is $1200, so your total payment will be $2200. Let's say we want to pay off the loan in 10 years (120 months), so we have a fixed principal payment of $1000/month. Further suppose that I want to pay a fixed amount of principal each month, rather than a fixed payment. Suppose I borrow $120000 at 1%/month interest (I know mortgages are usually priced with annual rates, but this will make the math simpler). All the other answers are great, but I thought I might add something concrete to clarify slightly.Ĭonsider a counterexample.
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