Find the accumulated amount A if the principal P is invested at the interest rate of r/year for t years. (Use a 365-day year. Round your answer to the nearest cent.)
P = $1800, r = 8
1
2
%, t = 8,
compounded annually

To find the accumulated amount $ A $ when a principal $ P $ is invested at an interest rate $ r $ for $ t $ years, compounded annually, we use the compound interest formula:

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

where:
- $ A $ is the accumulated amount (future value),
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the number of years,
- $ n $ is the number of times the interest is compounded per year (for annual compounding, $ n = 1 $).

### Given:
- $ P = 1800 $,
- $ r = 8 \frac{1}{2} \% = 0.085 $ (as a decimal),
- $ t = 8 $,
- $ n = 1 $ (since the interest is compounded annually).

### Step-by-Step Calculation:
\[
A = 1800 \left( 1 + \frac{0.085}{1} \right)^{1 \times 8}
\]
\[
A = 1800 \left( 1.085 \right)^8
\]
\[
A = 1800 \times 1.85093 \quad \text{(rounded to 5 decimal places)}
\]
\[
A \approx 3331.67
\]

### Final Answer:
The accumulated amount $ A $ is approximately **$3331.67**.

Would you like further details or have any questions?

### Related Questions:
1. What is the formula for compound interest when compounded quarterly?
2. How does the number of compounding periods per year affect the accumulated amount?
3. What would the accumulated amount be if the interest rate were 9% instead of 8.5%?
4. What is the difference between compound interest and simple interest for the same $ P $, $ r $, and $ t $?
5. How would the calculation change if interest were compounded monthly?

### Tip:
Always remember to convert the interest rate into decimal form by dividing by 100 before applying it in formulas.

Find the accumulated amount A if the principal P is invested at the interest rate of r/year for t years. (Use a 365-day year. Round your answer to the nearest cent.) P = $1800, r = 8 1/2%, t = 8, compounded annually.

Learn how to calculate the accumulated amount for a principal of $1800 invested at an interest rate of 8.5% over 8 years, compounded annually. This detailed guide walks through the compound interest formula, step-by-step calculations, and the final accumulated amount. Suitable for high school students in Grades 9-12.

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