Simple Interest vs Compound Interest
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Calculated on | Original principal only | Principal + accumulated interest |
| Formula | P × r × t | P × (1 + r/n)^(nt) - P |
| Growth over time | Linear (straight line) | Exponential (accelerating) |
| Total cost | Lower | Higher |
| Common uses | Short-term loans, some personal loans | Mortgages, LOCs, credit cards, savings |
Simple Interest Formula
Lenders in Canada use two main methods to calculate loan interest: simple interest and compound interest.
$$\text{Interest} = P \times r \times t$$
| Variable | Meaning | Example |
|---|---|---|
| P | Principal (amount borrowed) | $10,000 |
| r | Annual interest rate (decimal) | 0.06 (6%) |
| t | Time in years | 3 |
| Result | Total interest | $10,000 × 0.06 × 3 = $1,800 |
Compound Interest Formula
$$A = P \times \left(1 + \frac{r}{n}\right)^{n \times t}$$
| Variable | Meaning | Example |
|---|---|---|
| P | Principal | $10,000 |
| r | Annual interest rate (decimal) | 0.06 (6%) |
| n | Compounding periods per year | 12 (monthly) |
| t | Time in years | 3 |
| A | Future value (principal + interest) | $10,000 × (1 + 0.06/12)^(36) = $11,967 |
| Total interest | A - P | $1,967 |
Same Loan, Different Compounding
$10,000 at 6% for 3 years:
| Compounding | Total Interest Paid | Difference vs Simple |
|---|---|---|
| Simple | $1,800 | — |
| Annually | $1,910 | +$110 |
| Semi-annually | $1,941 | +$141 |
| Monthly | $1,967 | +$167 |
| Daily | $1,972 | +$172 |
Canadian Compounding Rules
| Loan Type | Compounding | Frequency | Set By |
|---|---|---|---|
| Mortgages (fixed) | Semi-annually | By law (Bank Act) | Federal regulation |
| Mortgages (variable) | Monthly | Industry practice | Lender |
| Lines of credit | Monthly or daily | Lender policy | Lender |
| Credit cards | Daily | Industry standard | Lender |
| Car loans | Monthly | Industry standard | Lender |
| Personal loans | Monthly | Industry standard | Lender |
| Student loans (federal) | Daily (floating) or monthly (fixed) | NSLSC policy | Federal |
| GICs / savings (earned) | Daily, monthly, or annually | Varies by product | Financial institution |
Converting Semi-Annual to Monthly Rate (Mortgages)
Canadian mortgages quote annual rates but compound semi-annually. To find the true monthly payment rate:
$$r_{\text{monthly}} = \left(1 + \frac{r_{\text{annual}}}{2}\right)^{1/6} - 1$$
Worked Example: 5% Mortgage
| Step | Calculation | Result |
|---|---|---|
| 1. Semi-annual rate | 5% ÷ 2 | 2.5% (0.025) |
| 2. Monthly equivalent | (1 + 0.025)^(1/6) - 1 | 0.004124 (0.4124%) |
| 3. Effective annual rate | 0.4124% × 12 | 4.949% |
The effective rate of 4.949% is less than 5% — semi-annual compounding benefits you vs. monthly compounding.
Amortization: How Loan Payments Work
Each payment is split between interest and principal. Early payments are mostly interest; later payments are mostly principal.
Worked Example: $300,000 Mortgage at 5%, 25-Year Amortization
| Payment | Total Payment | Interest Portion | Principal Portion | Remaining Balance |
|---|---|---|---|---|
| 1 | $1,745 | $1,237 | $508 | $299,492 |
| 12 | $1,745 | $1,214 | $531 | $293,578 |
| 60 (Year 5) | $1,745 | $1,112 | $633 | $268,091 |
| 120 (Year 10) | $1,745 | $959 | $786 | $229,408 |
| 180 (Year 15) | $1,745 | $769 | $976 | $181,467 |
| 240 (Year 20) | $1,745 | $529 | $1,216 | $122,758 |
| 300 (Year 25) | $1,745 | $7 | $1,738 | $0 |
| Metric | Value |
|---|---|
| Total payments over 25 years | $523,605 |
| Total interest paid | $223,605 |
| Interest as % of original loan | 74.5% |
Monthly Payment Formula
$$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$$
| Variable | Meaning |
|---|---|
| M | Monthly payment |
| P | Principal (loan amount) |
| r | Monthly interest rate (annual rate ÷ 12, adjusted for compounding) |
| n | Total number of payments (years × 12) |
Worked Examples by Loan Type
Car Loan
$30,000 at 6.5%, 5-year term, monthly compounding:
| Metric | Value |
|---|---|
| Monthly payment | $587 |
| Total payments | $35,220 |
| Total interest | $5,220 |
| Interest as % of loan | 17.4% |
Personal Loan
$15,000 at 9%, 3-year term, monthly compounding:
| Metric | Value |
|---|---|
| Monthly payment | $477 |
| Total payments | $17,172 |
| Total interest | $2,172 |
| Interest as % of loan | 14.5% |
Line of Credit
$10,000 balance at 7.5%, interest-only payments:
| Metric | Value |
|---|---|
| Monthly interest payment | $63 |
| Annual interest cost | $750 |
| Balance reduction | $0 (interest-only — need to pay extra to reduce principal) |
Credit Card
$5,000 balance at 19.99%, minimum payment (2% or $10):
| Metric | Value |
|---|---|
| Initial monthly interest | $83 |
| Time to pay off (minimums only) | 30+ years |
| Total interest paid | $8,000+ |
| Total cost | $13,000+ |
Interest Rate vs Total Cost
How rate affects total cost on a $300,000 mortgage, 25-year amortization:
| Interest Rate | Monthly Payment | Total Interest Paid | Total Cost |
|---|---|---|---|
| 3% | $1,419 | $125,756 | $425,756 |
| 4% | $1,578 | $173,362 | $473,362 |
| 5% | $1,745 | $223,605 | $523,605 |
| 6% | $1,919 | $275,798 | $575,798 |
| 7% | $2,099 | $329,596 | $629,596 |
Every 1% increase in rate costs roughly $50,000–55,000 more in interest over 25 years.
Tips to Reduce Interest Costs
| Strategy | How It Saves | Potential Savings |
|---|---|---|
| Make bi-weekly payments | 26 half-payments = 1 extra monthly payment/year | Shaves 2–3 years off mortgage |
| Increase payment amount | Extra goes directly to principal | Thousands in interest |
| Lump-sum payments | Large principal reductions when allowed | Significant over time |
| Shorter amortization | Less time for interest to accumulate | 30–40% less interest |
| Negotiate a lower rate | Direct impact on interest calculation | $50K+ over mortgage life |
| Pay more than minimum (credit cards) | Avoids “minimum payment trap” | Thousands vs. decades |