Compound Interest Calculator

Compound interest is the concept of earning interest on both the initial principal and the accumulated interest from previous periods. It is one of the most powerful forces in finance and a fundamental concept to understand for investing and savings.

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. A compound interest calculator helps you calculate the future value of an investment or loan, which is determined by the initial balance, the interest rate, the frequency of compounding, and the time the money is invested or borrowed for.

Types of Compound Interest

• Annual Compounding: The interest is calculated once per year.
• Semi-Annual Compounding: The interest is calculated twice a year.
• Quarterly Compounding: The interest is calculated four times a year.
• Monthly Compounding: The interest is calculated twelve times a year.
• Daily Compounding: The interest is calculated each day of the year.

Formula for Compound Interest

The compound interest formula is an equation that illustrates the value of $1000 after 1 year at an annual interest rate of 5% compounded annually.

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

Where:

• A = the future value of the investment
• P = the principal investment amount
• r = annual interest rate (in decimal)
• n = number of times that interest is compounded per year
• t = the time the money is invested for, in years

Example of Compound Interest

Example: If you invest $1000 (P) in a savings account with an annual interest rate of 5% (r=0.05), and the interest is compounded quarterly (n=4), for a period of 6 years (t), using the formula, we get:

A = 1000(1 + 0.05/4)^(4*6)

A = 1000(1 + 0.0125)^(24)

A = 1000 * 1.347

A = $1347.35

So, the balance after 6 years is $1347.35.

Continuous Compounding

In some cases, interest is compounded continuously rather than at regular intervals. The formula for continuous compounding is:

Formula: A = Pe^(rt)

Example: If you invest $1000 (P) at an interest rate of 5% (r=0.05) for 6 years (t), using the continuous compound interest formula, we get:

A = 1000 * e^(0.05*6)

A = 1000 * e^(0.3)

A = 1000 * 1.34986

A = $1349.86

So, the balance after 6 years with continuous compounding is $1349.86.