Annual compound interest is a method used to calculate the interest on an initial principal (the original amount of money) that also earns interest on previously accumulated interest, compounded once per year. The formula for compound interest is:

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

Where:

• $A$ = the amount of money accumulated after $n$ years, including interest
• $P$ = the principal (initial amount of money)
• $r$ = annual interest rate (in decimal form, so 5% would be 0.05)
• $n$ = the number of times interest is compounded per year (for annual compounding, $n = 1$)
• $t$ = the number of years the money is invested or borrowed for

Since we're considering annual compound interest, $n = 1$, simplifying the formula to:

$A = P \left(1 + r\right)^t$

Example:

If you invest $1000 at an interest rate of 5% for 3 years, the amount after 3 years would be:

$A = 1000 \left(1 + 0.05\right)^3 = 1000 \times 1.157625 = 1157.63$

So, after 3 years, the total amount would be $1157.63, which includes $157.63 of interest.

Would you like further clarification or details on this concept?

Here are 5 related questions you might find helpful:

1. How is compound interest different from simple interest?
2. What happens if the interest is compounded monthly instead of annually?
3. How do you calculate the principal when the final amount and interest rate are known?
4. What effect does increasing the interest rate have on compound interest over time?
5. How can you determine the time required to double your money with compound interest?

Tip: The longer your investment stays in a compound interest account, the more your money grows due to the effect of "interest on interest."