You deposit $300 in an account earning 8% interest compounded annually. How much will you have in the account in 10 years?


To calculate the future value of a deposit with compound interest, we use the formula:

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

where:
- $ A $ = the amount of money in the account after $ t $ years (future value)
- $ P $ = the principal amount (initial deposit) = \$300
- $ r $ = the annual interest rate (decimal) = 8% = 0.08
- $ n $ = the number of times interest is compounded per year = 1 (since it's compounded annually)
- $ t $ = the number of years = 10

Plugging in the values:

\[
A = 300 \left(1 + \frac{0.08}{1}\right)^{1 \times 10}
\]

Simplifying:

\[
A = 300 \left(1 + 0.08\right)^{10}
\]

\[
A = 300 \times (1.08)^{10}
\]

Now, let's calculate the value:

\[
A \approx 300 \times 2.15892 \approx 647.68
\]

So, you will have approximately **\$647.68** in the account after 10 years.

Would you like more details or have any questions? Here are some related questions:

1. How does the frequency of compounding affect the final amount?
2. What would the final amount be if the interest were compounded quarterly?
3. How much interest is earned over the 10 years?
4. What is the formula for continuous compounding interest?
5. How would the amount change if the interest rate were 10% instead?

**Tip:** The more frequently interest is compounded, the more the final amount will grow due to the effect of compound interest.


You deposit $300 in an account earning 8% interest compounded annually. How much will you have in the account in 10 years?

Learn how to calculate the future value of $300 deposited in an account earning 8% interest compounded annually. This detailed solution covers the compound interest formula and demonstrates the exponential growth of your investment over 10 years. Suitable for Grades 9-12 students and beyond.

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