Interest on Interest: How Compound Interest Works

This compound interest calculator estimates how much interest you earn on savings when previously earned interest remains in the account. Enter a starting balance, annual interest rate, and time; it shows the ending balance and the interest earned, assuming interest is compounded monthly.

Formula

Yes. When interest is left in an account and the account compounds, later interest can be calculated on both the original deposit and interest already credited. That is called compound interest, or informally, “interest on interest.” The calculator uses the compound-growth formula:

A = P × (1 + r)ⁿ

• A is the ending balance in dollars.
• P is the starting balance in dollars.
• r is the interest rate per compounding period, entered here as the annual percentage rate divided by 1,200 to get a monthly decimal rate.
• n is the number of monthly periods, calculated as years × 12.

The calculator’s second output is interest earned: A − P. It keeps the full calculated balance for the interest calculation, then displays the results rounded to cents. The model assumes one fixed annual rate and monthly compounding, with no later deposits or withdrawals.

Worked Example

Using the defaults—$10,000 starting balance, 5% annual interest, and 10 years—the monthly rate is 0.05 ÷ 12 = 0.0041667, and there are 10 × 12 = 120 monthly periods.

1. Ending balance: $10,000 × (1 + 0.05 ÷ 12)¹²⁰ = $16,470.09.
2. Interest earned: $16,470.09 − $10,000 = $6,470.09.

The balance includes interest that remained in the account and itself contributed to later growth. If interest were not added to the balance, or were withdrawn as it accrued, this calculation would not describe the account’s ending balance.

How Interest on Interest Works

With simple interest, interest is calculated only on the original principal. With compound interest, credited interest becomes part of the balance used for later calculations. For example, at a hypothetical 5% annual rate compounded once a year, a $1,000 balance earns $50 in the first year. If that $50 stays in the account, the second year’s 5% is calculated on $1,050, producing $52.50 rather than $50.

The difference may look modest over a short time, but compounding repeats. The effect depends on the starting amount, rate, how often interest is credited, and how long the balance remains invested. A calculator’s result is a mathematical projection, not a guarantee that an account will pay a particular rate.

Compounding Frequency and Account Terms

Compounding frequency describes how often accrued interest is added to the balance. This calculator assumes monthly compounding, a common modelling convention, but actual account terms can differ. If an account compounds daily, quarterly, or annually, its result may not match this monthly estimate even when the stated annual rate looks the same.

Read the account’s terms to determine how it defines the rate, credits interest, and handles changes in rates. The calculator treats the entered annual percentage as a nominal annual rate divided by 12. It does not convert an effective annual yield into a monthly rate. Those rate descriptions are not always interchangeable, so use a rate that matches the calculation assumptions.

When to Use This Estimate

Use this calculation to understand the growth of a starting deposit when there are no additional contributions, withdrawals, fees, or rate changes. It can illustrate how time and reinvested interest affect an account balance, or provide a baseline for checking an estimate against account disclosures.

It does not model regular deposits. If you add money over time, each deposit has its own period in which to earn interest, so a single starting-balance calculation will not capture the full result. Similarly, withdrawals reduce the amount that can compound. Taxes, account charges, promotional terms, and changing rates can also change the amount ultimately retained; none is included here.

Common Misunderstandings and Limits

• Interest is not always automatically reinvested. The interest-on-interest effect applies only when credited interest remains in the balance or is otherwise reinvested.
• More frequent compounding does not mean a higher stated rate. Frequency affects the mathematical result for a given nominal rate, but account rate terminology and terms must be checked separately.
• A projection is not a promised return. A variable rate can change, and actual credited interest may be affected by account-specific rules or charges.
• Rounding can cause small differences. The formula calculates using unrounded values and rounds displayed dollar amounts to cents. An institution may calculate and post interest using a different method or rounding schedule.

The calculator also excludes inflation, so the displayed balance is a future dollar amount rather than an estimate of what that amount will buy. It is not a loan calculator: although borrowers may also face interest charged on accumulated balances, loan schedules involve payments and terms that this savings-growth formula does not represent.

Frequently Asked Questions

Is interest paid on interest previously earned?
It can be. If interest is credited to an account and remains there, later interest may be calculated on the increased balance, including the earlier interest. The account’s compounding terms determine how this works.

What is the difference between simple and compound interest?
Simple interest is calculated on the original principal alone. Compound interest includes previously credited interest in the balance used for later interest calculations.

Does interest compound if I withdraw it?
Interest that you withdraw is no longer part of that account’s balance, so it cannot earn further interest there. The remaining balance may still compound under the account’s terms.

Does this calculator include monthly deposits?
No. It assumes a single starting balance and no later deposits or withdrawals. Regular contributions require a calculation that accounts for each contribution’s timing.

Why is my account balance different from the estimate?
The actual account may use another compounding or crediting schedule, a changing rate, fees, or other terms. Check its statement and disclosures for the figures and method that apply.

Assumptions

• Annual rate is fixed throughout the time entered.
• No deposits or withdrawals occur after the starting balance.
• Interest compounds monthly and is retained in the balance.
• Fees, taxes, inflation, and account-specific adjustments are not included.

This result is an estimate; the account’s disclosures give the applicable terms and exact figures.

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in p | Starting balance | $ | 10000 | 0 | 100000000
in apr | Annual interest rate | % | 5 | 0.01 | 100
in yrs | Time invested | years | 10 | 0.0833 | 50
out bal | Ending balance | $ | p * (1 + apr / 1200) ^ (yrs * 12) | 2
out int | Interest earned | $ | p * (1 + apr / 1200) ^ (yrs * 12) - p | 2