Savings and investing guide
Simple vs. Compound Interest: How Growth Is Calculated
Simple interest is calculated on the original principal; compound interest is calculated on principal plus previously earned interest. For a one-year deposit at the same rate, the results can match. Over multiple periods, compounding can produce a larger balance because interest can earn interest.
The difference in one sentence
With simple interest, each period’s interest is based on the starting principal. With compound interest, earned interest stays in the account and may be included in the balance used for the next interest calculation. The account agreement determines the actual rate, compounding schedule, fees, and treatment of deposits.
Formulas and assumptions
For a lump sum with simple interest, use A = P(1 + rt), where P is principal, r is the annual rate as a decimal, and t is years. For compound interest with m compounding periods per year, use A = P(1 + r/m)^(mt). These formulas assume a constant rate, no fees or taxes, and no additional deposits. A variable-rate account needs a period-by-period model instead.
A $1,000 example
At a hypothetical 5% annual rate for three years, simple interest gives $1,000 × (1 + 0.05 × 3) = $1,150. If interest compounds annually, the balance is $1,000 × 1.05³ = $1,157.63 after rounding. The $7.63 difference is caused by the two years of interest earning additional interest; it is not a promised return.
When the distinction matters
The gap generally grows with time, rate, and compounding frequency, though the specific account terms matter. For borrowing, interest that capitalizes or compounds can increase the amount owed. Compare the contract’s stated APR, compounding rules, payment schedule, and fees rather than relying on the word “compound” alone. Taxes and investment risk can also affect realized growth.
Use a projection carefully
Try several rates and time horizons to understand sensitivity. Treat the result as a scenario, not a forecast. For investments, returns are uncertain and may be negative; for savings, the rate may change. The calculator models its stated periodic assumptions and does not estimate taxes, fees, or inflation unless an input explicitly accounts for them.
| Method | Calculation | Ending balance |
|---|---|---|
| Simple interest | $1,000 × (1 + 0.05 × 3) | $1,150.00 |
| Annual compounding | $1,000 × 1.05³ | $1,157.63 |
Frequently asked questions
Can simple and compound interest be equal?
For a one-period calculation on the same principal and rate they can match; over multiple periods compound interest can earn interest on prior interest.
Does more frequent compounding always change the result?
For a positive constant nominal rate and identical horizon, more frequent compounding can increase the mathematical balance, but actual products define their own rate and crediting terms.
Sources and further reading
Try the calculator
Use the Compound Interest Calculator to explore your own numbers with the assumptions shown in the tool.
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Educational content only; not individualized financial, tax, or legal advice.