How the bank calculates your debt payments

Published by Graham on

Let’s get a few terms straight first:

If you would like to follow along, here is a great loan amortization calculator to use for your own amortization calculations.

The Calculation

When one borrows money, the person or company lending it needs to be paid some sort of interest rate or they will have no incentive to lend in the first place. There is a chance the borrower will not pay back the money so the lender also needs a reward for taking that risk. More importantly, the lender’s money could be used for other productive investments so if their money is tied up in a loan they should be compensated for their opportunity cost. However, the interest rate you pay on your loan is not a straight forward percentage of each monthly payment. No, no… it’s a bit more complicated than that. The formula used to calculate your total monthly loan repayment is as follows:

 A = periodic payment amount
p = portion of repayment that pays down the principal of your loan
i = interest rate per period
n = total number of payments

In a typical, straight forward fixed loan (meaning, the interest rate stays the same for the duration of the loan) the barrower pays a combination of (1) principal and (2) interest. Principal payment is the amount that goes toward paying down the loan balance, interest goes to the lender’s pockets. The monthly amount that the borrow repays stays constant, as defined by the calculation above, while the proportion of interest to principal over the life of a loan changes. A 30 year loan, for example, looks something like this:

Term = 30 years (paid monthly)

Loan = $300,000

Interest = 6%

6% of $300,000 is only $18,000 so how do you end up paying $347,515 in interest? The answer is simple: your 6% interest rate is recalculated against the balance you owe after every payment and since your balance is slowly paid down each payment period, the 6% is assessed against a smaller and smaller figure. This is known as the Annual Percentage Rate (APR). Using the same variables as above, the first few years of payments look like this:

Annual Percentage Yield (APY) vs Annual Percentage Rate (APR)

We calculated APR above, but you’re probably used to hearing about APY with regards to financing. APY is the same as APR except it takes intra-year compounding into consideration. The APR is reported annually, but if you your payments occur and are calculated monthly, then you will pay just a little bit more by virtue of compounding interest; that’s when you get APY. Furthermore, lenders will often bake their fees and additional “points” into the deal thus increasing the overall loan value which is reflected in the APR but not the APY.

Types of Loans That Don’t Amortize

Not all types of loans use an amortization schedule. Some are straight forward interest rate times loan balance. Such loans include:

  • Credit cards
  • Interest only loans
  • Balloon loans
Categories: Uncategorized