Compound Interest Calculator

How to Calculate Compound Interest

Compound interest is a powerful financial concept where you earn interest not only on your initial investment but also on the accumulated interest over time. This calculator helps you determine the future value of your investment considering both the initial principal and any additional contributions you make.

Compound Interest Formula

The basic compound interest formula is:

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

Where:

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

For additional contributions, we use the future value of a series formula:

$$FV = PMT \times \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}} \times \frac{n}{m}$$

Where:

• FV = Future value of additional contributions
• PMT = Additional contribution amount
• m = Number of contributions per year

Calculation Steps

1. Calculate the future value of the initial investment using the basic compound interest formula.
2. If there are additional contributions, calculate their future value using the future value of a series formula.
3. Add the results from steps 1 and 2 to get the total future value.
4. Calculate the total contributions by adding the initial investment to the sum of all additional contributions.
5. Subtract the total contributions from the total future value to determine the interest earned.
6. Calculate the Annual Percentage Yield (APY) using the formula: APY = (1 + r/n)^n - 1

Example Calculation

Let's calculate the compound interest for an investment with the following terms:

• Initial Investment (P) = $10,000
• Additional Monthly Contribution = $100
• Annual Interest Rate (r) = 5% = 0.05
• Compounding Frequency (n) = 12 (monthly)
• Time Period (t) = 10 years

Step 1: Calculate future value of initial investment

A = 10000(1 + 0.05/12)^(12 * 10) = $16,470.09

Step 2: Calculate future value of additional contributions

FV = 100 × ((1 + 0.05/12)^(12 * 10) - 1) / (0.05/12) = $15,528.23

Step 3: Calculate total future value

Total Future Value = $16,470.09 + $15,528.23 = $31,998.32

Step 4: Calculate total contributions

Total Contributions = $10,000 + ($100 × 12 × 10) = $22,000

Step 5: Calculate total interest earned

Total Interest Earned = $31,998.32 - $22,000 = $9,998.32

Step 6: Calculate APY

APY = (1 + 0.05/12)^12 - 1 = 5.12%

Therefore, after 10 years, the investment will grow to $31,998.32, earning $9,998.32 in interest. The APY is 5.12%.

Visual Representation

This diagram illustrates the growth of your investment over time. The blue area represents your contributions (initial investment plus additional contributions), while the green area shows the interest earned. As you can see, the power of compound interest becomes more evident over time, with the interest earned accelerating in later years.