Now can you calculate using same method
Use the compound interest formula to find the account balance A, where P is principal, r is interest rate, n is number of compounding periods per year, t is time, in years , and A is account balance
P=$54,116
r=8.5%
compounded=Quarterly
t=2.5

The account balance is approximately ?
(Simplify your answer. Type an integer or decimal rounded two decimal places as needed)

To find the account balance $ A $ using the compound interest formula, we use the following formula:

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

where:
- $ P $ is the principal amount,
- $ r $ is the annual interest rate (in decimal form),
- $ n $ is the number of compounding periods per year,
- $ t $ is the time the money is invested for in years,
- $ A $ is the account balance.

Given:
- $ P = 54,116 $ dollars,
- $ r = 8.5\% = 0.085 $ (in decimal form),
- $ n = 4 $ (compounded quarterly),
- $ t = 2.5 $ years.

First, substitute the given values into the compound interest formula:

\[ A = 54,116 \left(1 + \frac{0.085}{4}\right)^{4 \times 2.5} \]

Next, calculate the value inside the parentheses:

\[ \frac{0.085}{4} = 0.02125 \]

Now, add 1 to this value:

\[ 1 + 0.02125 = 1.02125 \]

Raise this value to the power of $ 4 \times 2.5 $:

\[ 4 \times 2.5 = 10 \]

So, we need to calculate:

\[ 1.02125^{10} \]

Using a calculator, we find:

\[ 1.02125^{10} \approx 1.233 \]

Now, multiply this result by the principal amount:

\[ A = 54,116 \times 1.233 \]

Finally, perform the multiplication:

\[ A \approx 54,116 \times 1.233 \approx 66,714.02 \]

Therefore, the approximate account balance is $ \boxed{66,714.02} $ dollars.

Do you want details or have any questions? Here are some additional related questions:

1. What happens to the account balance if the interest rate increases to 10%?
2. How does the account balance change if the interest is compounded monthly instead of quarterly?
3. What will be the account balance after 5 years with the same conditions?
4. How does continuous compounding affect the final amount?
5. If $ P $ were $100,000, what would the account balance be after 2.5 years with the same interest rate and compounding frequency?
6. What is the formula for calculating the amount of interest earned over the investment period?
7. How does the time period affect the final account balance in compound interest?
8. What is the effect of doubling the principal amount on the final balance?

**Tip:** Always convert interest rates to decimal form before using them in calculations.

Learn how to calculate compound interest using the formula A = P(1 + r/n)^(nt). Given P = $54,116, r = 8.5%, compounded quarterly, and t = 2.5 years, find the account balance A. Understand the step-by-step calculation process and its applications.

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