Simple interest is paid only on the original amount: interest = principal × rate × years. Compound interest is also paid on interest already earned: balance = principal × (1 + rate ÷ n)n × years, where n is how many times a year it compounds. At 6% for 5 years, 10,000 earns 3,000.00 simple interest, or 3,382.26 compounded yearly.
The difference looks small over a year or two and becomes large over decades, which is why it matters for savings, pensions and long loans. This guide shows both formulas with worked numbers, what compounding frequency does, and how APR and the effective annual rate fit in.
Simple interest
Interest = P × r × t, and the final amount is A = P × (1 + r × t).
P is the principal, r the yearly rate as a decimal (6% = 0.06) and t the time in years. 10,000 at 6% for 5 years earns 10,000 × 0.06 × 5 = 3,000.00, for a final amount of 13,000.00. The interest is the same every year, because it is always worked out on the original 10,000.
Simple interest is used for some short-term loans, some car finance and bond coupons that are paid out rather than reinvested. Each year’s interest is a simple percentage of a number.
Compound interest
A = P × (1 + r ÷ n)n × t
With yearly compounding (n = 1), 10,000 at 6% grows like this: 10,600 after one year, then 6% of 10,600 is added to give 11,236, and so on. After 5 years: 10,000 × 1.065 = 13,382.26. That is 382.26 more than simple interest, earned entirely as interest on interest.
Each year multiplies the balance by the same factor, which is the same reason successive percentage changes multiply rather than add.
| Years | Simple | Compound (yearly) | Difference |
|---|---|---|---|
| 1 | 10,600.00 | 10,600.00 | 0.00 |
| 2 | 11,200.00 | 11,236.00 | 36.00 |
| 5 | 13,000.00 | 13,382.26 | 382.26 |
| 10 | 16,000.00 | 17,908.48 | 1,908.48 |
| 20 | 22,000.00 | 32,071.35 | 10,071.35 |
| 30 | 28,000.00 | 57,434.91 | 29,434.91 |
How often it compounds
The more often interest is added, the sooner it starts earning interest itself. Monthly compounding of 6% gives 10,000 × (1 + 0.06 ÷ 12)60 = 13,488.50 after 5 years. The gains from more frequent compounding shrink quickly, and continuous compounding is the upper limit.
| Method | Balance after 5 years | Interest earned |
|---|---|---|
| Simple interest | 13,000.00 | 3,000.00 |
| Compounded yearly | 13,382.26 | 3,382.26 |
| Compounded quarterly | 13,468.55 | 3,468.55 |
| Compounded monthly | 13,488.50 | 3,488.50 |
| Compounded daily (365) | 13,498.26 | 3,498.26 |
| Compounded continuously | 13,498.59 | 3,498.59 |
Nominal rate, effective rate and APR
A “6% a year, compounded monthly” rate is a nominal rate. What you actually earn or pay over a year is the effective annual rate (EAR, sometimes AER for savings or APY in the US):
EAR = (1 + r ÷ n)n − 1
| Compounding | Effective annual rate |
|---|---|
| Yearly | 6.000% |
| Quarterly | 6.136% |
| Monthly | 6.168% |
| Daily | 6.183% |
| Continuous | 6.184% |
The APR on a loan is a legally defined annual rate that usually also folds in certain fees, so it is not always the same as the EAR, and the exact definition varies by country. When comparing savings accounts, compare the effective rate; when comparing loans, compare the APR from the same jurisdiction.
How loan interest works
A standard mortgage or personal loan charges interest each month on the balance still owed. Each payment covers that month’s interest first, and the rest reduces the balance — so early payments are mostly interest and later ones mostly principal. A 250,000 loan at 6.5% over 30 years costs 1,580.17 a month and 318,861.22 in total interest. The loan calculator shows the payment and the first year of the schedule for your own figures.
The rule of 72
To estimate how long money takes to double with compound interest, divide 72 by the rate in percent. At 6%: 72 ÷ 6 = 12 years. The exact answer is 11.9 years. The rule works well for rates between about 4% and 12%.
Common mistakes
- Multiplying the yearly rate by the number of years for compound growth. 6% for 10 years is not 60% growth; compounded yearly it is about 79%.
- Using the rate as a whole number. 6% is 0.06 in every formula.
- Mixing periods. With monthly compounding, divide the rate by 12 and multiply the years by 12.
- Comparing a nominal rate with an effective one. Convert both to the effective annual rate first.
- Forgetting tax and inflation. Interest is often taxed, and inflation reduces what the final balance can buy.
This guide is for general education, not financial advice.