Compound vs Simple Interest: What's the Difference

The mechanical difference

Simple interest is calculated only on the original principal. The interest itself does not earn interest. The formula:

A = P × (1 + r × t)

$10,000 at 5% simple interest for 10 years: A = $10,000 × (1 + 0.05 × 10) = $15,000. You earned $500 each year, for 10 years. Linear.

Compound interest is calculated on the principal plus all previously accumulated interest. The formula:

A = P × (1 + r)^t

$10,000 at 5% compounded annually for 10 years: A = $10,000 × (1.05)^10 = $16,289. You earned the same $500 in year one, but $525 in year two (5% of $10,500), and $551 in year three (5% of $11,025). Exponential.

The difference after 10 years is $1,289 — meaningful but not dramatic. The difference grows fast with time.

How the gap widens over time

Side-by-side comparison: $10,000 at 7%, simple vs compound, across horizons.

• 1 year: simple = $10,700, compound = $10,700. Identical.
• 5 years: simple = $13,500, compound = $14,026. Compound ahead by 4%.
• 10 years: simple = $17,000, compound = $19,672. Compound ahead by 16%.
• 20 years: simple = $24,000, compound = $38,697. Compound ahead by 61%.
• 30 years: simple = $31,000, compound = $76,123. Compound ahead by 146%.
• 40 years: simple = $38,000, compound = $149,745. Compound ahead by 294%.

At short horizons the two are nearly equivalent. At long horizons they diverge wildly. The reason is that simple interest is a straight line (y = mx + b), while compound interest is an exponential curve. Lines and exponentials are close near the origin and diverge forever.

Where each one shows up in real life

Simple interest — common in:

• Auto loans (most US). Interest accrues daily on the outstanding balance but does not compound. This is why paying early on a car loan reduces total interest.
• Bonds. Coupon payments are simple interest on face value.
• Short-term personal loans. Many are simple interest by design.
• Treasury bills. Discount securities with simple-interest pricing.

Compound interest — dominates in:

• Savings accounts and CDs. Interest is paid periodically and added to the balance, where it begins earning interest itself.
• Credit cards. Compound daily. Carry a balance and interest begins earning interest within the billing cycle.
• Mortgages. Most fixed-rate mortgages compound monthly.
• Student loans (after capitalization events). Accrued simple interest may be capitalized — added to the principal — at key events (end of grace period, refinancing), after which it effectively compounds.
• Investments. Reinvested dividends and capital appreciation compound by nature.

Why borrowers prefer simple and savers prefer compound

Compound interest is a mechanism for the owner of money to be rewarded for time. If you are the owner — a saver — that works in your favour. If you are renting money — a borrower — it works against you.

On a $20,000 auto loan at 6% over 5 years, simple interest means total interest of about $3,199 (since payments reduce the balance and interest is daily simple). The same loan compounded monthly would cost about $3,200 — nearly identical, because the term is short. The compounding disadvantage is small on a 5-year loan.

On a $300,000 mortgage at 6% for 30 years, compounding monthly yields total interest of about $347,500 — more than the principal itself. If that same mortgage had somehow been structured as simple interest on the original balance (it would never be), the interest would be $540,000. But because mortgage payments reduce principal over time, most of the simple-vs-compound gap is actually paid over the amortization schedule.

The real danger of compound interest for borrowers is unpaid interest that capitalizes. Miss a credit-card payment and the interest added to the balance begins generating interest of its own. Student loans that defer interest during school but capitalize it at graduation turn simple-accrued interest into compound debt overnight. These are the moments where compounding stops being an abstract formula and starts costing real money.

A 10-second sanity check

When you encounter a loan or investment, ask three questions:

1. Is it simple or compound? The contract should state it. If not, ask.
2. If compound, how often? Daily, monthly, quarterly. More frequent = slightly more expensive for borrowers, slightly more valuable for savers.
3. Can unpaid interest capitalize? This is the hidden trap. Simple-interest loans can behave like compound ones if missed interest is added to principal.

For savings: always want compound, want it as frequently as possible, and want to reinvest automatically.

For borrowing: prefer simple, avoid compounding capitalization events, pay down high-compound debt (credit cards especially) as a priority.

The short version

Simple interest is linear, compound interest is exponential. At 1 year they are equal; at 40 years they can differ by a factor of 4 or more. The math favours whoever holds the money — which is why savers want compound and borrowers want simple. Both are legal and both have legitimate uses. The problem is not which one exists; the problem is not knowing which one you signed up for.