Simple Interest Calculator Canada

What is simple interest?

**Simple interest is interest calculated only on the original principal amount, not on any previously earned interest.** The formula is I = P x r x t, where I is the interest, P is the principal, r is the annual interest rate expressed as a decimal, and t is the time in years.

For example, if you invest $10,000 at 5% simple interest for 3 years, the interest earned is $10,000 x 0.05 x 3 = $1,500. The total amount at the end is $11,500. Each year earns exactly $500 in interest, no more and no less, because the interest is never added to the principal.

Simple interest produces linear growth. If you graph the balance over time, you get a straight line. This is fundamentally different from compound interest, which produces a curve that accelerates upward because each period's interest is calculated on a growing base.

The formula can be rearranged to solve for any variable. To find the principal: P = I / (r x t). To find the rate: r = I / (P x t). To find the time: t = I / (P x r). The calculator above handles all four modes automatically.

Simple interest vs compound interest

**Simple interest grows linearly while compound interest grows exponentially, and the gap widens dramatically over time.** On $10,000 at 5% for 10 years, simple interest earns $5,000 while compound interest (monthly) earns $6,470. That is a 29% difference. Over 30 years, simple interest earns $15,000 while compound interest earns $34,677, a 131% difference.

The key distinction is what happens to earned interest. With simple interest, the $500 earned in year one does not generate its own interest in year two. With compound interest, that $500 becomes part of the new principal, and in year two you earn interest on $10,500 instead of $10,000.

For borrowers, simple interest is generally more favorable because total interest costs are lower. For investors, compound interest is more beneficial because your money works harder over time. Many financial products in Canada use compound interest, but some use simple interest.

When comparing products, always check which method applies. A "5% simple interest" GIC and a "5% compounded annually" GIC produce different returns. Over 5 years on $10,000, the simple interest GIC pays $2,500 while the compounded GIC pays $2,763.

When does simple interest apply in Canada?

**Several common financial products in Canada use simple interest rather than compound interest.** Understanding which method applies to your loan or investment helps you calculate the true cost or return.

**Treasury bills (T-bills):** The Government of Canada issues T-bills with 3-month, 6-month, and 12-month terms. T-bills are sold at a discount and redeemed at face value, and the return is calculated using simple interest. The Bank of Canada publishes weekly auction results with yields expressed as simple interest rates.

**Short-term loans and promissory notes:** Many personal loans, especially short-term ones from private lenders, use simple interest. The Interest Act (R.S.C., 1985, c. I-15) requires that all interest rates in Canadian contracts be expressed as annual rates, making simple interest the natural expression.

**Some GICs:** While most Canadian GICs compound annually, some non-redeemable GICs pay interest out periodically (monthly, semi-annually, or annually) rather than compounding it. When interest is paid out instead of reinvested, the effective calculation is simple interest.

**Auto loans:** Most Canadian car loans use simple interest amortization. Your monthly payment covers the interest accrued since the last payment plus some principal. Paying early reduces total interest because it reduces the principal balance faster.

**Student loans:** Canada Student Loans and most provincial student loans accrue interest using simple interest during the grace period and non-repayment periods. The current federal floating rate is prime + 0%, which is applied as simple interest on the outstanding balance.

• ✓Government of Canada Treasury bills (3, 6, 12 months)
• ✓Short-term personal loans and promissory notes
• ✓Non-compounding GICs that pay interest out periodically
• ✓Canadian auto loans (simple interest amortization)
• ✓Student loans during grace and non-repayment periods
• ✓Bridge loans and some commercial lending products

The simple interest formula explained

**The formula I = P x r x t has three inputs that multiply together to produce the total interest.** Each variable has a specific meaning and unit requirement.

**P (Principal):** The initial amount of money. This is the starting balance of an investment or the original amount of a loan. If you deposit $10,000 into a savings product, P = 10,000.

**r (Annual Rate):** The annual interest rate expressed as a decimal. A 5% rate becomes 0.05 in the formula. If a product advertises "5% simple interest," you use r = 0.05.

**t (Time):** The time period expressed in years. For 6 months, t = 0.5. For 90 days, t = 90/365 = 0.2466. The calculator above handles the conversion automatically when you select months or days.

**To find the total amount (A):** A = P + I = P + (P x r x t) = P(1 + rt). This gives you the final balance after interest is added. On a $10,000 investment at 5% for 2 years: A = $10,000(1 + 0.05 x 2) = $10,000(1.10) = $11,000.

**Converting between time units:** For months, divide by 12 (e.g., 18 months = 1.5 years). For days, divide by 365 (e.g., 90 days = 0.2466 years). Some financial institutions use 360 days (the banker's year), but the standard in Canada is 365 days.

Worked examples

**Example 1: Calculating interest on a T-bill.** You purchase a $25,000 Government of Canada T-bill with a 182-day term at a yield of 4.25%. Using I = P x r x t: I = $25,000 x 0.0425 x (182/365) = $25,000 x 0.0425 x 0.4986 = $529.88. Your T-bill returns $25,529.88 at maturity.

**Example 2: Finding the rate on a short-term loan.** You borrowed $5,000 for 9 months and paid $187.50 in interest. What was the annual rate? Using r = I / (P x t): r = $187.50 / ($5,000 x 0.75) = $187.50 / $3,750 = 0.05 = 5.0% per year.

**Example 3: How long to earn a target amount.** You have $15,000 in a simple interest account paying 3.5% and want to earn $2,000 in interest. Using t = I / (P x r): t = $2,000 / ($15,000 x 0.035) = $2,000 / $525 = 3.81 years, or approximately 3 years and 10 months.

**Example 4: What principal is needed.** You want to earn $1,000 in interest over 2 years at 4% simple interest. Using P = I / (r x t): P = $1,000 / (0.04 x 2) = $1,000 / 0.08 = $12,500. You need to invest $12,500.