Monthly Compound Interest Calculator

What is Monthly Compound Interest?

Monthly compound interest is a method of calculating interest where the interest earned each month is added to the principal, so that in the following month, you earn interest on the original principal plus the interest from the previous month. This process continues each month, leading to exponential growth over time.

The Monthly Compound Interest Formula

The formula for calculating monthly compound interest is:

\[A = P(1 + \frac{r}{12})^n\]

Where:

• \(A\) = Final amount
• \(P\) = Principal amount (initial investment)
• \(r\) = Annual interest rate (in decimal form)
• \(n\) = Number of months

Step-by-Step Monthly Compound Interest Calculation

1. Identify the principal amount (P), annual interest rate (r), and number of months (n).
2. Convert the annual interest rate to a monthly rate by dividing by 12.
3. Convert the monthly rate to decimal form (divide by 100).
4. Add 1 to the monthly rate in decimal form.
5. Raise this sum to the power of the number of months.
6. Multiply the result by the principal amount.
7. Subtract the principal from the final amount to get the compound interest earned.

Example Calculation

Let's calculate the monthly compound interest for a principal of $1,000, an annual interest rate of 6%, over 12 months:

1. \(P = \$1,000\), \(r = 6\% = 0.06\), \(n = 12\) months
2. Monthly rate = \(0.06 \div 12 = 0.005\) or 0.5%
3. \(A = 1000(1 + 0.005)^{12} = \$1,061.68\)
4. Interest earned = \$1,061.68 - \$1,000 = \$61.68

Visual Representation

The green portion represents the principal ($1000), and the blue portion represents the monthly compound interest earned ($61.68) over 12 months.

Monthly compound interest is a powerful tool for growing your savings or investments over time. It's important to note that while it can work in your favor for savings and investments, it can also work against you with debts like credit cards or loans that compound monthly.