How is interest calculated?

Interest rates are a hot topic in the news after the Bank of Canada started raising its policy interest rate earlier this year. The Bank’s policy rate influences the prime rate set by individual financial institutions, which in turn determines the interest rates you receive as a customer on variable rate mortgages, loans, savings and investments.

Interest goes both ways – you can earn interest on savings and investments, and be charged interest on debts. But how are interest rates determined, and how is interest calculated on savings and loans? Read on to learn more.

What is interest?

Banks don’t lend out money for free – they’re businesses, after all. When it comes to things like mortgages, credit cards, student loans, personal loans, or home equity lines of credit (HELOCs), interest is the amount charged by lenders on top of the money you borrow.

When it comes to savings, interest is the amount a financial institution pays you to keep your money deposited with them, whether it’s in a chequing or savings account, tax-free savings account (TFSA), registered retirement savings plan (RRSP), guaranteed investment certificate (GIC), or bond. Interest rates are usually expressed as a percentage of the loan or deposit amount.

Interest rates can be fixed or variable, depending on the financial product. For example, credit cards have fixed rates – you either pay off your balance in full every month, or pay a set interest rate on your balance. HELOCs usually have a variable interest rate. Personal loans and mortgages can have fixed or variable interest rates.

While the Bank of Canada’s policy interest rate holds sway in the financial world, it’s ultimately up to individual banks, credit unions, and other financial institutions to set their own interest rates on the products and services they offer.

How do you calculate interest?

How interest is calculated depends on the individual financial product and whether simple or compound interest applies. The easiest way to calculate interest is using the simple interest formula:

Simple interest = P x R x T

P = Principal amount (the beginning balance)

R = Interest rate (expressed as a decimal)

T = Number of time periods (generally one-year time periods)

For example, let’s say you deposit $1,000 into a short-term investment with a 10% annual interest rate and a one-year term. Using the above formula:

Principal amount = 1,000

Interest rate = 0.10

Time period = 1

1,000 x 0.10 x 1 = $100. This means that when you deposit $1,000, you would earn $100 in interest in one year for a total of $1,100.

Simple interest and compound interest

Simple interest lives up to its name because it’s calculated once annually and based on the principal balance. Simple interest usually applies to things like short-term loans and investments. With loans, this means that when you make regular payments and the balance gets smaller, interest is only calculated on the remaining balance. With savings and investments, interest is only calculated on the principal balance.

For that reason, simple interest doesn’t live up to the potential of what you could earn or owe because it only applies to the principal amount.

Compound interest, on the other hand, has a snowball effect. Interest is continually added to the total and included in calculating further interest – that’s why compounding is often described as “interest on interest.” For example, if you have a savings account that earns interest every month or year, the interest that account earns will also earn interest over time, and so on.

Compound interest is generally applied to things like chequing accounts, savings accounts, and credit cards. Compound interest is very useful for helping you reach your financial goals because the “interest on interest” effect helps grow your savings accounts quicker compared to simple interest.

Compound interest is calculated by using the following formula: A = P(1 + r/n)nt

A = Accrued interest (principal + interest)

P = Principal (the beginning balance)

r = Annual interest rate (expressed as a decimal)

n = Number of compounding periods per unit of time (daily, weekly, monthly, etc.)

t = Time in years (expressed as a decimal)

Using a similar loan to our simple interest calculation, here’s how compound interest would work if you deposit $1,000 into an investment with a 10% annual interest rate and a one-year term, with interest compounding monthly.

P = 1,000

r = 0.10

n = 12

t = 1

Using these numbers, we can figure out how much compound interest you would accrue in a year:

A = P(1 + r/n)ntA = 1,000(1 + 0.1/12)(12)(1)A = 1,000(1 + 0.0083333333333333)(12)A = $1,104.71

After one year, you would earn $104.71 in interest on top of your initial $1,000 balance, for a total of $1,104.71. The difference between simple vs. compound interest is small in this example ($100 vs. $104.71), but compounding interest has the potential to add up over longer periods of time.

If you find it hard to calculate interest manually because math isn’t your strong suit, you can always use a calculator to figure out simple or compound interest. There are plenty of online interest calculators to do the work for you.

Other factors to consider when calculating interest

Whether you’re doing it manually or using a calculator, it’s fairly easy to calculate simple interest or compound interest when you’re talking about straightforward debt repayment or savings accounts with a fixed interest rate over a defined period of time.

Other types of debt such as mortgages have loan terms and amortization periods that can change the amount of interest you pay. For example, you can have a mortgage with a 25-year amortization (the total life of your mortgage) split up into shorter terms. Let’s say you currently have a 5-year fixed rate mortgage. After five years, your term is up and it’s time to renew. Interest rates could be higher or lower, which will change the amount you pay in interest.

Of course, if you have a mortgage or loan with a variable interest rate, it can be difficult to calculate interest because there’s the possibility that your interest rate may change in the future. When the Bank of Canada raises or lowers its policy interest rate, it subsequently affects the interest rates on financial products out there in the market.

It’s important to understand how interest is calculated because interest rates affect the cost of borrowing and the returns you get on your savings. Interest can be very helpful in building wealth, but can also be very detrimental to paying down debt if you’re barely making your minimum payments and interest keeps adding up. Whenever you sign up for products like a savings account or loan, make sure you know the interest rate and how interest is calculated to know how much interest you’ll be paying or receiving in return.