The formula you’re looking at is the compound interest formula, commonly used in finance to calculate the future value of an investment or loan with interest that compounds over time.

Compound Interest Formula

The formula: $F = P \left(1 + \frac{r}{n}\right)^{nt}$

where:

• F = the future value of the investment/loan, including interest
• P = the principal amount (the initial sum of money)
• r = the annual interest rate (decimal form, e.g., 5% would be 0.05)
• n = the number of times interest is compounded per year
• t = the number of years the money is invested or borrowed for

Explanation of Each Part

• $\frac{r}{n}$ adjusts the annual rate to reflect how often interest is applied within the year.
• $nt$ is the total number of times interest compounds over the entire duration.
• The term $\left(1 + \frac{r}{n}\right)^{nt}$ grows over time as interest compounds, meaning interest is calculated on the accumulated amount rather than just the initial principal.

Example

If you invest $1,000 at a 5% annual interest rate, compounded monthly for 3 years, the future value F would be calculated as: $F = 1000 \left(1 + \frac{0.05}{12}\right)^{12 \times 3}$

Would you like a step-by-step solution for an example, or do you have any questions?

Related Questions

1. How does compound interest differ from simple interest?
2. How does increasing the compounding frequency (n) impact the final amount (F)?
3. What happens when interest compounds continuously instead of periodically?
4. Can this formula be rearranged to solve for the interest rate (r)?
5. How would changing the number of years (t) affect the future value?

Tip:

To quickly estimate compound interest, remember the "Rule of 72" – divide 72 by the interest rate to approximate the years needed to double an investment with annual compounding.