Compound Interest Formula: Calculate Growth Over Time

The compound interest formula is A = P(1 + r/n)^nt, where the initial amount earns interest on both the principal and previously credited interest. Enter a starting balance, annual rate, time, and compounding frequency to estimate the ending balance, interest earned, and total contributions.

Formula

The standard formula for a fixed annual rate compounded a set number of times per year is:

A = P(1 + r/n)^nt

• A is the ending balance, in dollars.
• P is the starting principal, in dollars.
• r is the annual interest rate as a decimal, such as 0.05 for 5%.
• n is the number of compounding periods per year.
• t is the time in years.

In the calculator, the rate is entered as a percentage, so it uses apr / 100 to convert it to a decimal. The periodic rate is therefore apr / (100 × n), and the number of periods is n × yrs. The interest earned is the ending balance minus the starting balance; it does not include any additional deposits or withdrawals.

Worked Example

Using the calculator’s default values—$1,000 starting balance, 5% annual interest, 10 years, and monthly compounding (12 periods per year)—the calculation is:

1. Convert the annual percentage rate to a decimal: 5% = 0.05.
2. Find the monthly rate: 0.05 / 12 = 0.0041666667.
3. Count the periods: 12 × 10 = 120 months.
4. Substitute into the formula: A = 1,000 × (1 + 0.05/12)¹²⁰.
5. Calculate and round to cents: A = $1,647.01.
6. Subtract the principal: $1,647.01 − $1,000 = $647.01 interest earned.

The calculator rounds the displayed results to two decimal places. Calculations made with a rounded periodic rate at intermediate steps may differ slightly, so retain full precision until the final rounding.

Assumptions

• The annual rate stays fixed throughout the period.
• Interest is credited at the end of each compounding period; no money is added or withdrawn.
• Compounding occurs at the frequency entered. For example, 12 means monthly and 4 means quarterly.
• Fees, taxes, inflation, and changes in the rate are not included.

How Compounding Works

With simple interest, each period’s interest is calculated only on the original principal. With compound interest, credited interest becomes part of the balance used to calculate later interest. That is why growth can accelerate over time: the balance earning interest gets larger as interest accumulates.

For example, if $1,000 earns 5% for a year with annual compounding, it becomes $1,050. In the second year, 5% applies to $1,050, not just the original $1,000. The formula accounts for this repeating process by raising the one-period growth factor, (1 + r/n), to the total number of periods, nt.

The annual percentage rate entered here is treated as a nominal annual rate divided evenly across the chosen periods. For monthly compounding at 5%, the formula applies 5% / 12 each month. The result is an estimate under that convention, not a guarantee of what an account or investment will pay.

Choosing the Compounding Frequency

Use the frequency at which interest is actually credited or compounded, if known. Common mathematical choices include:

• Annually: n = 1
• Semiannually: n = 2
• Quarterly: n = 4
• Monthly: n = 12
• Daily: n = 365 in this calculator

For the same stated annual rate and time, more frequent compounding generally produces a slightly higher balance because interest is added to the balance sooner. The difference depends on the rate and duration; it is not a separate bonus rate. If a contract or account uses a different day-count convention, leap-year method, or continuous compounding, this calculator may not match its exact calculation.

Using the Result and Understanding Limits

The ending balance shows the calculated principal plus interest under the selected assumptions. “Interest earned” is only the increase attributable to the formula; it is not a measure of purchasing power. Inflation can reduce what a future dollar buys, while fees or taxes can change an actual net result. Those factors need separate information and are not estimated here.

This version models one initial deposit and no later cash flows. If regular contributions are made, each contribution has its own time to compound, so use a formula or calculator designed for recurring deposits rather than simply adding all contributions to the starting balance. Withdrawals likewise reduce the balance available to earn future interest.

Rates and periods must use consistent units: the rate is annual, time is in years, and n is periods per year. Entering 5 for a 5% rate is correct in the calculator; entering 0.05 would mean 0.05%, not 5%. A period count of 12 means twelve periods each year, not twelve periods in total. The result is an estimate; account or investment disclosures provide the exact figures and applicable terms.

Frequently Asked Questions

What is the compound interest formula?
A = P(1 + r/n)^nt. P is the starting principal, r is the annual rate as a decimal, n is compounding periods per year, and t is years.

How do I calculate compound interest in Excel?
For a fixed rate and no additional deposits, enter a formula equivalent to =P*(1+r/n)^(n*t), replacing each symbol with a cell reference or number. Convert a percentage such as 5% to 0.05 if the formula expects a decimal.

Does more frequent compounding always increase the result?
For the same positive nominal annual rate and duration, increasing the number of compounding periods generally raises the calculated ending balance, because interest is credited sooner. The actual account’s stated method and terms still matter.

What is the difference between compound and simple interest?
Simple interest is calculated on the original principal only. Compound interest is calculated on the current balance, including interest already credited, so the interest base can grow over time.

Can this formula include monthly deposits?
Not by itself. It assumes one starting amount and no subsequent deposits or withdrawals. A recurring-contribution calculation must account for each payment’s amount, timing, and compounding period.

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in p | Starting balance | $ | 1000 | 0 | 100000000
in apr | Annual interest rate | % | 5 | 0 | 100
in yrs | Time | years | 10 | 0 | 100
in n | Compounding periods per year | - | 12 | 1 | 365
out total | Ending balance | $ | p * (1 + apr / (100 * n)) ^ (n * yrs) | 2
out int | Interest earned | $ | total - p | 2