Simple and compound interest start from the same deposit and the same rate, and in the first year they usually give the same answer. They separate only once earned interest starts earning interest of its own. The clearest way to see how large that separation becomes is to run one deposit through both models and read the results side by side.
One deposit, two models, six horizons
Take 10,000 currency units at 8% a year. Under simple interest, every year's interest is 8% of the original 10,000, so the balance rises by exactly 800 a year. Under compound interest with annual compounding, each year's 8% is charged on the balance at the start of that year, which already includes earlier interest. The monthly column uses the same 8% nominal rate split into twelve 0.6667% steps.
| Years | Simple interest | Compound, annual | Compound, monthly | Annual compound minus simple |
|---|---|---|---|---|
| 1 | 10,800.00 | 10,800.00 | 10,830.00 | 0.00 |
| 3 | 12,400.00 | 12,597.12 | 12,702.37 | 197.12 |
| 5 | 14,000.00 | 14,693.28 | 14,898.46 | 693.28 |
| 10 | 18,000.00 | 21,589.25 | 22,196.40 | 3,589.25 |
| 20 | 26,000.00 | 46,609.57 | 49,268.03 | 20,609.57 |
| 30 | 34,000.00 | 100,626.57 | 109,357.30 | 66,626.57 |
P is the starting principal, r the annual rate as a decimal (0.08), t the time in years and n the number of compounding periods per year. With n = 1 and t = 1, both formulas reduce to P × 1.08, which is why the first row matches.
Why the gap starts small and then dominates
Simple interest draws a straight line: 800 in year one, 800 in year thirty. Compound interest adds 8% of a rising number: 800 in year one, 864 in year two, and 7,453.82 in year thirty, because by then the starting balance for that year is 93,172.75. The rate never changed; the base it applies to did.
After 10 years the compound account has earned 11,589.25 of interest against 8,000 under simple interest, about 45% more. After 30 years it has earned 90,626.57 against 24,000, nearly four times as much. Most of the difference arrives late, which is why the early rows can make compounding look unimportant.
Monthly compounding adds a further 8,730.73 over 30 years compared with annual compounding. Frequency matters, but far less than whether interest compounds at all. The guide on nominal and effective annual rates shows how to compare frequencies on one scale.
Compound Interest CalculatorRun your own principal, rate and term with annual, quarterly, monthly or daily compounding.Saving toward a target usually involves new deposits as well as interest. This comparison holds the starting principal fixed; the monthly savings needed for a goal example instead shows how a target date, an existing balance and regular contributions fit together. Use that model when the practical question is how much to put aside each month.
When simple interest describes what really happens
Simple interest is the accurate model whenever interest leaves the balance instead of staying in it.
- Payouts you spend. A deposit that pays its profit or interest out monthly or quarterly never grows its principal if you spend each payment. Whatever the account's stated compounding, your earnings follow the simple-interest line.
- Bond coupons taken as cash. A coupon is a fixed percentage of face value, so the income stream is simple interest on face value. What happens on the price side is a separate question that yield to maturity answers.
- Short periods. For three months at 8%, simple interest is 10,000 × 0.08 × 0.25 = 200. The simple-interest calculator accepts fractional years; the compound calculator accepts whole years only.
- Flat-rate loan quotes. Some lenders compute the total charge on the original amount for the full term, even though you repay as you go. The arithmetic is simple interest, but the true cost is much higher than the quoted rate, as the flat-rate versus reducing-balance guide shows.
When compound interest is the right model
- Savings where interest is credited to the balance and left alone.
- Investments whose income is reinvested, such as dividends used to buy more units.
- Debt where unpaid interest is added to what you owe, such as a credit card balance carried from month to month.
- Long-range projections of a single lump sum, where the late compounding rows above decide the outcome.
An installment loan that charges interest on the unpaid balance fits neither picture neatly. Each month's interest is calculated on what is still owed, and each payment reduces that amount. Its cost is shown by an amortization schedule rather than either formula; see how to read an amortization schedule.
Amortization CalculatorSee how a declining-balance loan splits each payment between interest and principal.A quick test for which model a quote uses
- Ask whether interest is credited to the balance or paid out to you. Credited and left in place means compounding.
- Look for a stated compounding frequency or an effective rate. A product that names neither and pays out monthly is earning simple interest on the principal.
- Compare year two with year one. If the second year's interest equals the first year's, the product is simple. If it is larger by the first year's interest times the rate (800 × 0.08 = 64 here), it compounds annually.
- For a loan, ask whether interest is charged on the original amount or on the remaining balance.
What these worked examples leave out
Both models here hold the rate fixed and assume no deposits, withdrawals, fees or taxes. A tax withheld on each interest payment reduces what is left to compound, so the after-tax compound line sits below the one shown. Real accounts may accrue interest daily on a changing balance and credit it monthly. Investment returns are not a steady 8%; a volatile series that averages 8% grows less than 8% compounded, which the CAGR, ROI and average return guide works through. None of the figures are adjusted for inflation.