Compound Interest Calculator

What is Compound Interest?

Compound interest is interest calculated on the initial principal and also on the accumulated interest from previous periods. Albert Einstein reportedly called it "the eighth wonder of the world." Unlike simple interest, which only earns on the original amount, compound interest lets your money grow exponentially over time.

The Compound Interest Formula

• A = Final amount
• P = Principal (initial investment)
• r = Annual interest rate (decimal)
• n = Number of times compounded per year
• t = Number of years

Example

If you invest $10,000 at 7% annually compounded monthly for 10 years: $A = 10000(1 + 0.07/12)^{120} = $20,096.61$. Your money doubles in about 10 years.

How to use this calculator

1. Enter the starting amount, which is the principal \(P\).
2. Type the annual interest rate as a decimal or percent, depending on the calculator setting, as \(r\).
3. Choose how often interest is compounded each year, \(n\), such as monthly, quarterly, or yearly.
4. Enter the time in years, \(t\), then calculate to find the final amount \(A\).

The formula explained

The formula \(A = P\left(1 + \frac{r}{n}\right)^{nt}\) computes the final amount after compound interest is applied. It tells you how a starting amount grows when interest is added \(n\) times per year for \(t\) years.

• A = final amount after interest is added
• P = principal, or the starting amount
• r = annual interest rate as a decimal
• n = number of compounding periods per year
• t = time in years

Step by step method

1. Start with the principal \(P\).
2. Divide the annual rate \(r\) by \(n\) to get the rate per compounding period, then add \(1\).
3. Raise that result to the power \(nt\), then multiply by \(P\) to find \(A\).

Worked example

Problem. You deposit \(\$2,000\) at an annual interest rate of \(5\%\), compounded monthly, for \(3\) years. Find the final amount.

1. Use \(P = 2000\), \(r = 0.05\), \(n = 12\), and \(t = 3\).
2. Substitute into the formula, \(A = 2000\left(1 + \frac{0.05}{12}\right)^{12 \cdot 3}\).
3. This gives \(A \approx 2322.19\).

Tips and common mistakes

• Make sure the interest rate is entered as a decimal, so \(5\%\) becomes \(0.05\).
• Check the compounding frequency carefully, because monthly, quarterly, and yearly compounding can give different results.

Frequently asked questions