Compound Interest Calculator Overview

What Is Compound Interest?

Compound interest is interest that is calculated on both your original deposit and on any interest that has already been credited. Simple interest only ever applies to the principal, so it grows in a straight line. Compound interest grows exponentially, because every period the base it is calculated from gets slightly larger.

The practical effect is that a small difference in rate or a few extra years can produce a surprisingly large difference in the final balance. That is why compounding is usually described as the most important concept in long-term investing.

How Compound Interest Is Calculated

For a single lump sum with no additional deposits, the future value is:

A = P × (1 + r / n)^{n × t}

where P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the number of years.

When you add regular contributions, there is no single tidy formula, because each deposit compounds for a different length of time. This calculator builds the schedule period by period instead. Between two contributions, the balance grows by a factor that depends on how many compounding periods fit into that stretch:

Balance_next = Balance × (1 + r / n)^{n / m} + Contribution

where m is the number of contributions per year. When the contribution frequency and the compounding frequency match, the exponent is exactly 1 and the result is the familiar per-period compounding formula. When they differ, the exponent scales the growth to the shorter interval, which keeps the maths consistent across every combination of settings.

How Regular Contributions Affect Growth

Recurring deposits do two things at once. They increase the amount of money working for you, and they keep increasing it on a schedule. Because each deposit starts compounding immediately, early contributions are worth far more than late ones. A deposit made in year one has the entire investment period to grow; a deposit made in the final year barely compounds at all.

The optional annual contribution increase models the common habit of raising your savings rate alongside your income. Even a modest yearly bump compounds into a meaningfully larger balance over a long horizon.

Why Compounding Frequency Matters

More frequent compounding produces a slightly higher effective annual rate. At the same nominal rate, daily compounding returns more than monthly compounding, which returns more than annual compounding. The difference is small at low rates and short horizons, but it widens as the rate and the time frame grow.

The gap between the nominal rate and the effective rate is what the phrase "annual percentage yield" describes. This calculator reports the effective annual rate alongside your results so you can see the real return your settings produce.

Assumptions and Limitations

• The interest rate is held constant for the entire period.
• Contributions are deposited at the end of each contribution period.
• No taxes, fees, withdrawals, or inflation adjustments are modelled.
• Interest is credited without rounding at each period; totals may differ by a few cents from institutions that round per period.
• Results are projections based on the inputs you supply, not guarantees of future performance.