Neil opened a savings account and deposited $500.00 as principal. The account earns 10% interest, compounded annually. What is the balance after 9 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.

To calculate the balance after 9 years, we will use the compound interest formula:

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

Where:
- $A$ = final amount (balance),
- $P$ = principal amount (initial deposit),
- $r$ = annual interest rate (as a decimal),
- $n$ = number of times interest is compounded per year,
- $t$ = number of years.

### Given:
- $P = 500$,
- $r = 10\% = 0.10$,
- $n = 1$ (since interest is compounded annually),
- $t = 9$ years.

Now, substitute the values into the formula:

\[
A = 500 \left(1 + \frac{0.10}{1}\right)^{1 \times 9}
\]
\[
A = 500 \left(1 + 0.10\right)^9
\]
\[
A = 500 \times (1.10)^9
\]

Let's calculate the value.The balance in the account after 9 years, with 10% interest compounded annually, will be **$1178.97**.

Would you like more details or have any questions? Here are five related questions to explore:

1. What would the balance be if the interest was compounded semi-annually?
2. How does the balance change if the interest rate is reduced to 5%?
3. What is the formula to calculate simple interest, and how does it compare to compound interest?
4. How much total interest was earned over the 9-year period?
5. What would happen if Neil made an additional deposit each year?

**Tip:** The more frequently interest is compounded, the more interest you earn due to the effects of "compounding on compounding."

Neil opened a savings account and deposited $500.00 as principal. The account earns 10% interest, compounded annually. What is the balance after 9 years? Use the formula A = P(1 + r/n)^(nt), where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.

Calculate the compound interest on a $500 savings account at 10% interest, compounded annually, over 9 years. This detailed solution covers the compound interest formula and explains how to find the balance after 9 years. Ideal for high school students learning about exponential growth and interest calculations.

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