Simple interest is calculated on the original principal—the starting amount of money—while compound interest is calculated on a balance that includes previously accumulated interest. That difference lets interest itself earn interest when it stays in the account and is compounded.
To see the effect clearly, hold the starting amount, rate and time period constant. In a hypothetical example with €1,000 earning 5% annually for three years, annual compounding produces about €7.63 more than simple interest, before fees and taxes and with no additional deposits or withdrawals.
What changes when interest compounds
With simple interest, the calculation base stays fixed. If the principal and rate remain unchanged, the same amount of interest accrues each period. Interest earned in earlier periods does not enter the calculation for later periods.
With compound interest, earned interest is added to the balance, a process called capitalization. The next interest calculation uses that larger balance. Under a fixed positive rate, each successive period therefore earns more interest than the previous one. These are the calculation bases described by Banco Sabadell.
The practical question is what happens to the interest after it is earned. Interest paid out and kept separate does not compound within the original balance. Interest retained and capitalized becomes part of the amount used for subsequent calculations.
The formulas—and why the rate period matters
Both formulas start with the same inputs:
- P is the original principal.
- r is the interest rate written as a decimal: 5% becomes 0.05.
- t is the length of time, measured in units that match the rate.
- I is the interest earned.
- A is the ending amount, including principal and interest.
Simple interest
For a fixed annual rate over a term measured in years, the simple-interest formula explained by Bankinter is:
I = P × r × t
Add the interest to the principal to find the ending amount:
A = P × (1 + r × t)
This is linear growth: each additional year adds the same amount of interest when the principal and annual rate stay fixed.
Compound interest
With a fixed annual rate and annual compounding, the compound-interest formula explained by BBVA is:
A = P × (1 + r)^t
The symbol ^ means “raised to the power of.” For a three-year term, the balance is multiplied by (1 + r) three times. To find interest alone, subtract the original principal: I = A − P.
Here, t counts annual compounding periods. If a rate is quoted per month instead, the calculation must use the monthly rate and the number of monthly periods. Using an annual rate with a count of months would calculate a different result.
A worked example with matching assumptions
Raisin’s published comparison uses a hypothetical €1,000 principal, a fixed 5% annual rate and a three-year term. The compound-interest calculation capitalizes interest once a year. Neither calculation includes additional contributions, withdrawals, fees, taxes or rate changes. The euro amounts are illustrative, not an account offer.
| Calculation method | Starting principal | Annual rate | Term | Interest earned | Ending balance | Capitalization |
| Simple interest | €1,000 | 5% | 3 years | €150.00 | €1,150.00 | Interest is not capitalized |
| Compound interest | €1,000 | 5% | 3 years | €157.63 | €1,157.63 | Once a year |
Amounts are rounded to the nearest cent after calculating the final result.
Under simple interest, the calculation is €1,000 × 0.05 × 3. Each year earns €50 because the calculation always starts from the original €1,000.
Annual compounding begins the same way: the first year earns €50. In the second year, however, 5% applies to €1,050, generating €52.50. The third year applies 5% to €1,102.50, generating €55.125 before rounding.
The exact compound ending amount is €1,157.625. Subtracting the simple ending amount of €1,150 gives a difference of €7.625, or about €7.63. The extra amount comes entirely from interest earned on earlier interest; the starting deposit, annual rate and term are unchanged.
Nominal annual rates and effective annual growth
Compounding frequency determines how often earned interest enters the balance. Annual compounding does this once a year; monthly compounding does it 12 times.
A nominal annual rate supplies the annual rate used to calculate periodic interest. Effective annual growth measures the total percentage increase over one year after compounding. At the same positive nominal annual rate, more frequent capitalization produces greater effective annual growth under otherwise identical, fee-free assumptions.
For a fixed nominal annual rate r, compounded m times per year over t years, the balance calculation is:
A = P × (1 + r/m)^(m × t)
Consider a separate hypothetical case: a 5% nominal annual rate compounded monthly, with all interest retained, no deposits or withdrawals, and no fees or taxes. The monthly rate is 0.05 ÷ 12, or approximately 0.4167%. The effective growth over one year is:
(1 + 0.05/12)^12 − 1 ≈ 5.116%
The balance grows by slightly more than 5% because interest credited during the year participates in later monthly calculations. By contrast, a 5% annual rate compounded once at year-end produces 5% growth over that year under the same fee-free assumptions.
Payment frequency is one of the factors the Banco de España identifies as affecting an effective annual calculation. The 5.116% result here isolates monthly capitalization; an actual product’s outcome also depends on its rate terms, charges and cash flows.
What changes the result outside a basic example
A useful comparison holds the calculation inputs constant before judging the effect of compounding. Changing the rate, term or deposits at the same time makes it harder to identify which change produced the difference.
Time and changing rates
Under a fixed positive rate, a longer term gives accumulated interest more opportunities to earn interest. But a fixed-rate illustration assumes the same rate throughout the calculation. Raisin notes that a savings account’s rate can change, so extending one advertised rate across many years may produce a result that differs from the account’s actual growth.
Long-term calculations also magnify the importance of checking the arithmetic. Raisin’s separate long-horizon table lists €33,000 for €10,000 earning 5% simple annual interest over 50 years. Applying those stated inputs gives €10,000 × (1 + 0.05 × 50) = €35,000. The annual interest is €500, totaling €25,000 over the term, plus the original principal.
Fees, access and investment risk
Compounding describes a calculation mechanism, not a particular investment or a guaranteed return. A savings account may capitalize interest according to its terms; investment returns can vary rather than follow the fixed positive rate used in these examples.
For someone choosing where to save, capitalization is therefore one consideration alongside the rate, fees, access conditions and risks. Being young or having no debt does not by itself determine which product is suitable. Fees and taxes can reduce the amount retained, while withdrawals can reduce the balance available to earn future interest.
The same mathematical mechanism can also increase an amount owed when unpaid interest is added to debt and later interest is calculated on that larger balance. A particular loan’s repayment schedule and contract determine how its balance develops; the single-deposit savings formulas do not capture every borrowing arrangement.
Additional contributions are separate from compounding
Reinvested interest comes from the existing balance. An additional contribution is new money added to it. Both can increase the ending amount, but they enter the calculation differently.
The basic compound formula assumes one starting principal. With regular contributions, each deposit needs its own timing in the calculation: money added earlier has more periods to earn interest than money added later. A balance that rises partly because of new deposits therefore reflects both contributions and growth on the money already invested.
