Simple vs compound interest explained

Start with $1,000, a sample 10% per year, and 3 years. Simple interest adds $100 each year on the original principal and ends at $1,300. Annual compound interest grows the balance with Add percent each year and ends at $1,331. The percentage calculator locks every step below. The rate is a teaching input, not a market quote.

The same principal, two rules

Simple interest always looks back at the starting principal.

interest_per_year = (rate ÷ 100) × principal
total_simple = principal + interest_per_year × years

Compound interest (once per year in this article) looks at the current balance.

balance_next = balance_now × (1 + rate ÷ 100)

Closed form for annual compounding, for checking the table:

balance = principal × (1 + rate ÷ 100) ^ years

1,000 × (1.10)³ = 1,331. That matches three Add percent steps in the tool.

Running example: year by year

Simple path

Yearly interest with Percent of: 10% of 1,000 = 100.

Total interest = 100 × 3 = 300. Ending balance = 1,000 + 300 = 1,300.

10% of 1,000 = (10 ÷ 100) × 1,000 = 100

Every year repeats that 100 because the base stays the original principal.

Compound path (annual)

Use Add percent with percent 10 and the growing base:

Interest earned: year 1 100, year 2 110, year 3 121. Total interest 331, which is $31 more than the simple path on the same headline rate and term.

Edge case: treating compound like simple

A common mistake is to take 10% of 1,000 three times (300) and call that “compound for three years,” ending at 1,300. That is the simple path again. True annual compounding needs the updated base each year, or the power form, ending at 1,331.

Another slip is to multiply the rate by years first (10% × 3 = 30%) and then Add percent once to 1,000 → 1,300. That again copies simple interest. Compounding is repeated growth on the balance, not one inflated percent on day one.

Why the gap is only $31 here

With round numbers and three years, the compound advantage is modest. Stretch the same sample 10% to more years and the gap widens because each new interest slice sits on a larger base. Change the sample rate and the dollar gap changes too. The lesson is the rule, not a forecast.

Bank and loan products may compound monthly or daily, charge fees, or use a reducing balance on debt. Those details are outside this running example. For installment loans that charge interest on a declining principal, see flat vs reducing-balance interest and the EMI calculator. This article stays with deposit-style simple vs annual compound on one principal.

Reading the two endings side by side

Both stories start at 1,000 and use the same sample 10% label. Simple pays you 100 three times because the base never grows. Compound pays 100, then 110, then 121 because each Add percent step feeds the next. If a brochure shows only an ending balance, ask whether interest was recalculated on the original principal or on the growing balance. Without that sentence, 1,300 and 1,331 look like a dispute about who mistyped a calculator, when they are two different contracts.

You can also reverse-check compound with percent change. From 1,000 to 1,331 the overall rise is larger than 30%, even though three simple 10% slices would suggest 30% on the original principal. That is expected: compounding is not “rate × years” as a single add percent.

Try the steps in the calculator

1. Open the percentage calculator.
2. Simple slice: Percent of, 10 and 1000 → 100.
3. Compound year 1: Add percent, 10 and 1000 → 1100.
4. Year 2: Add percent, 10 and 1100 → 1210.
5. Year 3: Add percent, 10 and 1210 → 1331.

For the bare arithmetic of “what is X% of Y” without a multi-year story, use how to calculate percentages. When you already have two balances and want the percent move between them, use percent change on the same tool.

Write the assumption next to any total you share: “simple, 3 years, 10% sample” or “compound annual, 3 years, 10% sample.” Without that label, 1,300 and 1,331 look like a disagreement instead of two different rules. Providers define compounding frequency in the product sheet. Match their frequency before you compare offers. This page does not quote live rates.

If you only need a single growth step (raise a balance by 10% once), Add percent is enough and you can stop. The multi-year table matters when someone claims “compounded for three years” while still multiplying the original principal each time. Rebuild year 2 and year 3 in the tool whenever that claim appears.