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 = $280,000
r = 3.5%
t = 3 compounded daily

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

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

Where:
- $ P $ is the principal amount ($280,000),
- $ r $ is the annual interest rate (3.5% or 0.035),
- $ n $ is the number of times the interest is compounded per year (365 for daily compounding),
- $ t $ is the time the money is invested for in years (3 years).

Substituting the values:

\[
A = 280,000 \left(1 + \frac{0.035}{365}\right)^{365 \times 3}
\]

Let's calculate this.The accumulated amount $ A $ after 3 years, with a principal of $280,000 invested at an interest rate of 3.5% compounded daily, is **$310,997.41**.

Would you like any further details or have any questions?

Here are some related questions you might find helpful:

1. What is the formula for compound interest if the interest is compounded semi-annually?
2. How would the accumulated amount change if the interest were compounded monthly instead of daily?
3. What is the effect of increasing the interest rate on the accumulated amount?
4. How would the accumulated amount differ if the investment period were extended to 5 years?
5. How is the formula for continuous compounding different from that for daily compounding?

**Tip:** When comparing different investments, always consider the compounding frequency, as it can significantly impact the accumulated amount.

Learn how to calculate compound interest with daily compounding using a principal of $280,000, an interest rate of 3.5% per year, compounded daily for 3 years. Discover the accumulated amount with step-by-step calculations and rounded to the nearest cent.

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