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How Interest Works on Loans and Savings (APR vs. APY)

By: Barry Choi

Anyone who’s borrowed or deposited money will have noticed that there’s always an interest rate involved. When it comes to loans, the interest rate represents how much you’re paying to borrow that money. As far as savings is concerned, the interest rate is how much money you’re earning by keeping your money deposited.

While interest rates are just a normal part of lending and saving, what most people don’t realize is that the rates can be calculated in different ways. There’s the Annual Percentage Rate (APR) and the Annual Percentage Yield (APY). These two calculations work in different ways, which is why you need to understand the difference between APR and APY.

How the annual percentage rate works

The annual percentage rate is commonly known as simple interest. Think of it as interest that’s accumulated over a period of one year. APR can apply to loans, deposits, or even credit cards.

Suppose you’re in the market for a new refrigerator that costs $1,000. You don’t have the funds upfront, but the store offers you financing with an interest rate of 15% APR. That means you would pay $150 in interest over the course of the year, or $12.50 each month.

While APR does include the interest rate, fees, and additional costs, what it leaves out are the compounding periods (if any). For example, a compound period could be semi-annually, quarterly, or even by a set number of days. Looking at APR only can be misleading since it might actually cost you more than you expected when borrowing.

How the annual percentage yield works

If you want to know the true cost of borrowing, you need to use the annual percentage yield. This calculation considers compounding periods which is interest on interest. Some people will also refer to this term as compound interest.

Compound interest is great when you’re earning interest on your savings, but it also increases the cost of borrowing when you get a loan. A good example is a mortgage in Canada which is compounded semi-annually. While you may be getting quotes of 5% interest, you would actually be paying 5.063%. The 5% quoted is the APR, while 5.063% is the APY rate.

Admittedly, in the case of mortgages, the difference between the two rates is minimal, but that’s because compounding only happens semi-annually. If the compounding period was more frequent, there could be a significant difference.

Comparing APR to APY

Okay, trying to keep track of acronyms and numbers can be a bit confusing at times. It might be easier to look at things side-by-side to see the difference. Suppose you’re going to deposit $10,000 into your bank account that pays 2% interest annually. Many people would assume that at the end of three years, they would have earned $600 in interest. While that’s a good assumption, you’d be forgetting that APY applies here as you would be earning interest on interest every year.

Years investedAPRAPY
End of year 1$10,200$10,200
End of year 2$10,400$10,404
End of year 3$10,600$10,612.08

When looking at APR and APY, you can clearly see that there is a difference when using APY to calculate interest. Some people think that the difference is so minor that it doesn’t matter, but again, it comes down to the compounding periods.

Let’s say you’re considering a loan from a payday lender. Instead of displaying the interest rate, they’ll advertise something along the lines of borrowing $100 for ten days for $44. That sounds like a good deal since you’re only paying $22 for each $100 or 22% (APR) interest, but it’s not that simple.

Your loan is for 10 days, but there are 365 days in a year. If you divide 365 by 10, you get the compounding period of 36.5. You now take that compounding period and multiply it by the interest rate which is 36.5 X 22%. That equals 803% interest. 

Clearly, that’s an incredibly high interest rate to be paying for a loan. If you knew those numbers in advance, it’s unlikely you would consider a loan at those terms. Why pay that much interest when there are better options available with lower rates?

The bottom line

Both APR and APY are used by financial institutions to describe interest rates. The main difference is the compounding periods. Generally speaking, financial institutions will usually display APR when you need to borrow and APY when it comes to savings since they appear more favourable. If you’re not sure how the numbers work, ask the lender/financial institution as it’ll affect how much you pay or save over longer periods of time.

Barry Choi is a personal finance and travel expert based in Toronto. He frequent media appearances Canada and the U.S. His website Money We Have is one of Canada's most trusted sources for all things related to money and travel. You can find him on Twitter: @barrychoi