Compound Interest Calculator

What is Compound Interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.

The Compound Interest Formula

The formula for calculating compound interest is:

\[A = P(1 + \frac{r}{n})^{nt}\]

Where:

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

Step-by-Step Compound Interest Calculation

1. Identify the principal amount (P), annual interest rate (r), compounding frequency (n), and time period (t).
2. Convert the annual interest rate to decimal form (divide by 100).
3. Plug these values into the compound interest formula.
4. Calculate the final amount (A).
5. Subtract the principal from the final amount to get the compound interest earned.

Example Calculation

Let's calculate the compound interest for a principal of $1,000, an annual interest rate of 5%, compounded quarterly, over 2 years:

1. \(P = \$1,000\), \(r = 5\% = 0.05\), \(n = 4\) (quarterly), \(t = 2\) years
2. \(A = 1000(1 + \frac{0.05}{4})^{4 \times 2} = \$1,104.94\)
3. Compound interest earned = \$1,104.94 - \$1,000 = \$104.94

Visual Representation

The green portion represents the principal ($1000), and the blue portion represents the compound interest earned ($104.94).