Compound Interest Calculator

A compound interest calculator shows how an investment or savings balance grows when interest is earned on the original amount and n previously accumulated interest. It is used by savers, investors, and anyone planning long-term financial goals who wants to see the real impact of time and rate on their money.

How to Use the Compound Interest Calculator

1. Enter your starting balance or initial deposit.
2. Enter the annual interest rate or expected return.
3. Set the compounding frequency: annually, quarterly, monthly, or daily.
4. Enter the number of years you plan to save or invest.
5. Optionally, add a regular monthly contribution to see how additional deposits accelerate growth.

The Formula

The compound interest formula is:

A = P x (1 + r/n)^(n x t)

Where A is the final amount, P is the principal (starting balance), r is the annual interest rate as a decimal, n is the number of times interest compounds per year, and t is the number of years. For regular contributions, each deposit is also compounded from the time it is added, so the total is the sum of the compounded principal and the future value of the contribution series.

Real-World Example

You invest $5,000 at an annual rate of 5%, compounded monthly, for 10 years with no additional contributions.

• r/n = 0.05 / 12 = 0.004167
• n x t = 12 x 10 = 120
• A = 5,000 x (1 + 0.004167)^120
• A = 5,000 x 1.6470 = approximately $8,235

You started with $5,000 and gained $3,235 purely from compound interest, without adding a single extra dollar. Over 20 years at the same rate, the balance would grow to approximately $13,600.

Why Compounding Frequency Matters

The more frequently interest is compounded, the more you earn. The difference between annual and daily compounding on a large balance over many years is meaningful. On $10,000 at 5% over 20 years, annual compounding produces approximately $26,533, while daily compounding produces approximately $27,181. The gap widens as the balance and time period grow. Most deposit accounts compound monthly or daily, while many investment accounts treat returns as annual. Always check the compounding frequency when comparing products, as it affects your real return.

Reference Table: Growth of a $10,000 lump sum

The table compounds a single $10,000 deposit at five rates over four periods, with interest added once a year and nothing withdrawn. Money doubles in roughly 72 divided by the annual rate, so 6% takes about 12 years.

Worked Example on Screen

The capture below shows Compound Interest Calculator after the inputs were entered, with the result on screen. Enter the same values to reproduce it.

Captured from solved.tools on 10 September 2026.

Frequently Asked Questions

What is the difference between compound and simple interest? Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all previously earned interest. Over long periods, compound interest produces significantly higher returns. A $10,000 investment at 5% simple interest for 20 years earns $10,000 in interest. The same sum at 5% compound interest (annually) earns approximately $16,533.

Does compound interest work against me on debt? Yes. When you carry a credit card balance or loan, interest compounds on the outstanding amount, including previous interest charges. This is why high-interest debt grows quickly if minimum payments are made. Paying more than the minimum reduces the principal faster and cuts the total interest owed.

What is the Rule of 72? The Rule of 72 is a quick way to estimate how long it takes to double your money. Divide 72 by the annual interest rate. At 6%, your money doubles in approximately 12 years. At 8%, it doubles in roughly 9 years. It is a useful mental shortcut before running the full compound interest calculation.

How does inflation affect compound growth? Compound interest calculators typically show nominal growth, not real growth. If your savings earn 4% annually but inflation is running at 3%, your real return is only around 1%. For long-term planning, subtract the expected inflation rate from your interest rate to see the purchasing power gain, not just the number in your account.

Also try these free tools:

• Savings Calculator
• Investment Calculator
• Rule of 72

The formula and its terms

Compound interest is written A = P times (1 + r/n) raised to the power n times t.

The terms are: A is the final balance, P is the starting principal, r is the annual interest rate as a decimal, n is the number of compounding periods in a year, and t is the time in years. When interest is added once a year, n is 1. When it is added monthly, n is 12. When it is added daily, n is 365.

The quantity r/n is the rate applied each period, and n times t is the total number of periods. Compounding works because each period applies the rate to a balance that already includes the previous period's interest.

Worked example: 10,000 at 6 percent for 10 years

Take a principal of 10,000, an annual rate of 6 percent, and a term of 10 years, with interest added monthly. The rate per month is 0.06 divided by 12, which is 0.005. The number of periods is 12 times 10, which is 120.

The balance is 10,000 times 1.005 raised to the 120th power. The factor 1.005 to the 120th power is 1.819397. Multiplying by 10,000 gives 18,193.97. The interest earned is 8,193.97, and the total is a little under 1.82 times the original.

The effect of compounding frequency

The same 6 percent rate over the same 10 years gives a different balance depending on how often the interest is added, because each added period starts earning interest sooner.

| Frequency | Periods a year | Final balance on 10,000 | | Annually | 1 | 17,908.48 | | Semi-annually | 2 | 18,061.11 | | Quarterly | 4 | 18,140.18 | | Monthly | 12 | 18,193.97 | | Daily | 365 | 18,220.29 |

Moving from annual to monthly compounding adds 285.49 over the decade. Moving from monthly to daily adds only 26.32 more. The gains shrink as the frequency rises, and there is a ceiling, which is the limit as the period count grows without bound.

The rule of 72

The rule of 72 estimates the years needed to double a sum: divide 72 by the annual percentage rate. At 6 percent the rule gives 12 years.

The exact doubling time is the natural logarithm of 2 divided by the natural logarithm of 1.06, which is 11.896 years. The rule overstates the time by about a month at this rate. The error grows as the rate rises, so the rule is a quick estimate for rates near the middle of the single digits and should give way to the exact formula outside that range.

Doubling time at several rates

| Rate | Rule of 72 | Exact years | | 3 percent | 24.0 | 23.45 | | 5 percent | 14.4 | 14.21 | | 6 percent | 12.0 | 11.90 | | 8 percent | 9.0 | 9.01 | | 10 percent | 7.2 | 7.27 |

The table shows why the rule is popular: within the common range it is close to the exact figure, and it can be worked in the head. Outside that range, at very low or very high rates, it drifts and the formula should be used instead.

Simple interest against compound interest

Simple interest pays on the original principal only, so the balance grows in a straight line. The formula is the interest equals the principal times the rate times the time. On 10,000 at 6 percent for 10 years, the simple interest is 10,000 times 0.06 times 10, which is 6,000, and the balance is 16,000.

Compound interest pays on the principal and on the interest already added, so the balance curves upward. The same 10,000 at 6 percent for 10 years, compounded monthly, reaches 18,193.97. The gap between the two, 2,193.97, is the compounding effect, and it grows with the rate and the term. Over 30 years at the same rate the gap becomes far larger than the simple interest itself.

What the calculator ignores

The formula models a single deposit left alone. It does not subtract tax on the interest, which in many countries reduces the effective rate. It does not subtract inflation, so the balance is in nominal money, and the real purchasing power grows more slowly. It does not model fees, which on a managed product can remove a large part of the compounding.

It also assumes the rate stays fixed for the whole term. In practice a rate can change, and a single average rate hides the path. It does not handle contributions or withdrawals made partway through, which change the balance that later interest is applied to; those need a deposit or withdrawal schedule rather than the single-sum formula.

Used for a single deposit and a fixed rate, the formula is exact. Used as a forecast for a real account, it is a clean upper bound that the costs above will pull down.

References

• Financial Conduct Authority, UK. https://www.fca.org.uk/
• Investopedia, "Compound Interest". https://www.investopedia.com/terms/c/compoundinterest.asp. Accessed 2026-09-26.
• Investopedia, "The Rule of 72". https://www.investopedia.com/terms/r/ruleof72.asp. Accessed 2026-09-26.
• U.S. Securities and Exchange Commission, investor.gov compound interest calculator and explanation. U.S. SEC Investor.gov, compound interest calculator. Accessed 2026-09-26.
• MoneyHelper (Money and Pensions Service), "Saving money". https://www.moneyhelper.org.uk/en/savings. Accessed 2026-09-26.