Head-to-head
Simple Interest vs Compound Interest
Both methods apply an interest rate to a balance. The difference is what counts as the balance. Simple interest always applies the rate to the original principal, so the interest earned each year is identical and never itself earns anything. Compound interest applies the rate to the principal plus whatever interest has already accumulated, so the interest starts earning interest.
That single difference produces a curve rather than a straight line, and the curve is flat at first. In year one the two methods agree exactly — there is no accumulated interest yet. By year ten, at 5%, compounding has added 25.8% more interest. By year thirty the ratio is closer to two to one. This is why compounding is described as slow then sudden, and why the comparison matters more the longer the term.
The two are not interchangeable descriptions of the same product. A savings account that quotes simple interest and one that quotes compound interest at the same nominal rate will pay different amounts, and a loan advertised at a low rate can cost more than a slightly higher one if the compounding frequency differs. The table below isolates the mechanism; the worked example puts real numbers on it.
Simple interest
How To Calculate Simple Interest
Simple interest pays only on the original principal and never reinvests itself. That makes it the easiest interest calculation to verify by hand — and the right model for most short-term loans, bonds and treasury bills.
Compound interest
How To Calculate Compound Interest
Compound interest is interest that earns interest. Once interest is added to your balance, that added amount starts earning too — which is why long horizons grow faster than people expect.
How They Differ
| Attribute | Simple interest | Compound interest |
|---|---|---|
| Interest is charged on | The original principal, unchanged | Principal plus accumulated interest |
| Formula | I = P × r × t | A = P(1 + r/n)^(nt) |
| Growth pattern | Linear — the same interest every period | Exponential — interest grows each period |
| Effect of a longer term | Total interest scales with time | Total interest accelerates with time |
| Effect of compounding frequency | None — frequency is irrelevant | More frequent compounding pays slightly more |
| Typical products | Car loans, some personal loans, short-term notes | Savings accounts, mortgages, credit cards, investments |
| Where it is used in this library | Working out a flat interest charge | Working out growth or amortisation over many periods |
The Same Numbers, Both Ways
$10,000 at 5% a year for 10 years, with interest compounding once a year.
- Principal
- $10,000
- Annual rate
- 5%
- Term
- 10 years
| Line | Simple interest | Compound interest |
|---|---|---|
| Balance after 1 year | $10,500.00 | $10,500.00 |
| Balance after 5 years | $12,500.00 | $12,762.82 |
| Balance after 10 years | $15,000.00 | $16,288.95 |
| Total interest earned | $5,000.00 | $6,288.95 |
| Extra from compounding | — | +$1,288.95 |
Compounding adds $1,288.95 over ten years, which is 25.8% more interest than the simple-interest version of the same deal. Both start from $10,000.00 at 5%; the only difference is that one method lets the interest earn interest.
When To Use Each
Simple interest
- The interest is paid out each period rather than reinvested — a bond coupon, or a loan where interest is settled monthly.
- The term is short enough that compounding has not had time to matter, typically under two years.
- A contract explicitly states a flat rate on the original amount, which is common on car finance and some personal loans.
Compound interest
- Interest stays in the account or on the balance and is charged or paid on the running total.
- The term is long — retirement savings, mortgages, student loans.
- You need to compare products that quote different compounding frequencies, because only the compound calculation normalises them.
Common Questions
Which one do banks actually use?
Almost always compound interest, at a frequency stated in the terms — daily for savings accounts and credit cards, monthly for most mortgages. Simple interest survives mainly in car finance and short-term lending, where it is quoted as a flat rate.
Is simple interest ever better for the borrower?
Yes, always, at the same nominal rate and term, because you pay interest on a smaller base. The catch is that simple-interest loans often carry a higher nominal rate precisely because the structure is cheaper for the borrower.
How much difference does compounding frequency make?
At 5% over one year, annual compounding gives 5.00%, monthly gives 5.12%, and daily gives 5.13%. The gap widens with the rate and the term, not with the frequency alone — which is why APY exists as a comparable figure.
Does the difference grow linearly?
No. The absolute gap grows faster than the term. At 5%, ten years produces a gap of $1,289 on $10,000; twenty years produces $6,533; thirty years produces $18,219.
What if interest is paid out but not withdrawn?
Then it is being reinvested, and the account is effectively compounding even if the headline product is described as simple interest. The distinction is about what happens to the interest, not what the label says.
More Comparisons
- ROI vs CAGR
ROI measures the whole return; CAGR turns it into a compound annual rate. A 100% return over five years is 20% a year by division but 14.87% a year in reality.
- APR vs APY
APR is the nominal annual rate; APY includes compounding. At 6% compounded monthly the gap is 0.17 points — $16.78 a year on $10,000, and $488 over five years.
- Markup vs Margin
Markup divides profit by cost; margin divides it by price. The same $20 profit is 50% markup and 33.3% margin — and the gap widens as the rate rises.
Sources
- Compound Interest Calculator — how compounding works — U.S. Securities and Exchange Commission, Investor.gov
- Truth in Lending Act — Regulation Z, annual percentage rate — Consumer Financial Protection Bureau
- Interest rates and compounding — consumer credit data — Board of Governors of the Federal Reserve System
Both methods sit in Finance.