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 = $270,000,
r = 4
1
2
%,
t = 3, compounded daily

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

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

where:
- $ P = 270,000 $ (the principal),
- $ r = 4.5\% = \frac{4.5}{100} = 0.045 $ (annual interest rate),
- $ t = 3 $ years (time period),
- $ n = 365 $ (number of compounding periods per year, since the interest is compounded daily).

Let's substitute the values and compute the accumulated amount $ A $.The accumulated amount $ A $ after 3 years, with a principal of $270,000 invested at an interest rate of 4.5% per year compounded daily, is **$309,022.36**.

Would you like further details, or do you have any other questions?

Here are some related questions you might be interested in:
1. How does the frequency of compounding affect the accumulated amount?
2. What would be the accumulated amount if the interest were compounded monthly instead of daily?
3. How can the formula for continuous compounding be used in this scenario?
4. What would the accumulated amount be if the interest rate was different, say 5%?
5. How can the effect of inflation on the accumulated amount be calculated?

**Tip:** Compounding more frequently (e.g., daily instead of monthly) generally results in a slightly higher accumulated amount.

Learn how to calculate the accumulated amount when $270,000 is invested at an interest rate of 4.5% per year, compounded daily for 3 years. Get the precise result rounded to the nearest cent. Explore the effects of daily compounding on investment growth.

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