Compound Interest Formula:

A = Pe(r/n)^(nt)

where:

• A is the future value of the investment.
• P is the principal amount invested.
• e is the mathematical constant, 2.718281.
• r is the annual interest rate.
• n is the number of times interest is compounded per year.
• t is the number of years the investment is made for.

Explanation:

• Principal (P) is the initial amount invested.
• Interest Rate (r) is the percentage of the principal that is charged as interest each year.
• Compound Interest Rate (r/n) is the annual interest rate divided by the number of times interest is compounded per year.
• Number of Years (t) is the number of years the investment is made for.
• The formula calculates the future value (A) of an investment based on the principal, interest rate, and number of years.

Example:

Suppose you invest $10,000 at an interest rate of 5% per year, compounded quarterly. After 10 years, the future value of your investment can be calculated as:

A = 10,000(1.05)^(4*10) = $16,285.02

Therefore, the future value of your investment after 10 years is $16,285.02.

Key Points:

• Compound interest is the interest calculated on an investment based on the principal and the accumulated interest.
• The formula for compound interest is A = Pe(r/n)^(nt).
• The higher the interest rate and the longer the investment period, the greater the future value.
• Compound interest can be used to calculate future value, present value, and future interest.