Simple and Compound Interest
Interest is the price of money over time. There are only two ways to charge it, and the difference between them grows enormous over long periods.
Simple interest is calculated on the original principal only. The amount earned is identical every period.
Interest = P × r × t Balance = P × (1 + r × t)
Compound interest is calculated on the principal plus all interest already earned, so each period earns slightly more than the last.
Balance = P × (1 + r ÷ n)n×t
where P is the principal, r the annual rate, t the number of years and n the compounding periods per year.
The Gap Between Them
$10,000 at 5%, simple against monthly compounding:
| Years | Simple | Compound (monthly) | Difference |
|---|---|---|---|
| 1 | $10,500 | $10,512 | $12 |
| 5 | $12,500 | $12,834 | $334 |
| 10 | $15,000 | $16,470 | $1,470 |
| 20 | $20,000 | $27,126 | $7,126 |
| 30 | $25,000 | $44,677 | $19,677 |
Over one year the difference is a few dollars. Over thirty it exceeds the original deposit. Simple interest grows in a straight line; compound interest grows exponentially, and exponential growth is almost invisible early and overwhelming late.
Where Each Is Used
| Simple interest | Compound interest |
|---|---|
| Most car loans (precomputed interest) | Savings and deposit accounts |
| Short-term personal loans | Credit card balances |
| Some bonds' coupon payments | Mortgages and most amortising loans |
| Certificates with simple accrual | Investment and retirement accounts |
The pattern is that borrowers usually face compounding and savers frequently do not — which is one reason paying off debt tends to beat saving at the same headline rate.
Compounding Frequency
The more often interest is added, the more the balance earns on itself. The gain shrinks quickly, though: moving from annual to monthly compounding at 5% adds about 0.116 percentage points of effective yield, while moving from daily to continuous adds under 0.001.
| Compounding | Effective annual rate at 5% nominal |
|---|---|
| Annually | 5.0000% |
| Semi-annually | 5.0625% |
| Quarterly | 5.0945% |
| Monthly | 5.1162% |
| Daily | 5.1267% |
| Continuously | 5.1271% |
Tax and Inflation
Two deductions apply to almost every real deposit, and both are available in the More Options section.
Tax on interest is normally charged as it is earned, which reduces the base that compounds. A 5% return taxed at 25% compounds as 3.75%, and the shortfall widens over time far more than the 1.25 percentage point gap suggests.
Inflation reduces what the final balance buys. A 5% return during 3% inflation is a real gain of about 1.94% — the exact figure from the Fisher equation, (1.05 ÷ 1.03) − 1, not the 2% that subtraction implies. During periods when inflation exceeds deposit rates, a savings account loses purchasing power despite the balance rising.
The Rule of 72
Dividing 72 by the interest rate approximates the years needed to double the money under compounding. At 5% that is 14.4 years against an exact 14.2; at 8%, 9 years against 9.006. The approximation is accurate between roughly 4% and 12%.
Interest and Debt
The same arithmetic works against a borrower. A $5,000 credit card balance at 22% APR compounded daily grows to roughly $6,230 after one year with no payments, and $9,700 after three. This is why eliminating high-interest debt is mathematically superior to investing at any plausible return — it is a guaranteed, tax-free 22%.
Frequently Asked Questions
Which should I choose if I have a choice?
As a saver, always compound, and as often as offered. As a borrower, simple interest is cheaper — though check whether early repayment reduces the interest, since precomputed simple-interest loans often do not refund it.
Why is my bank's interest slightly different?
Day-count conventions. Banks may use 360 or 365 days, credit interest on specific calendar dates, and round each posting. These differences are small per period and visible over long terms.
What is APY?
Annual percentage yield — the nominal rate adjusted for compounding, and the correct number for comparing savings accounts. APR is the borrowing equivalent and includes fees.
Does the contribution earn interest in the first year?
In this calculator contributions are added at the end of each year, so a given year's contribution starts earning the following year. That is the conservative convention.