Question

Calculate the compound amount. Use the compound amount formula and a calculator. (Round your answer to two decimal places.)
P = $9500, r = 8% compounded daily, t = 5 years

Answer 1

To calculate the compound amount using the formula for compound interest, we can use the formula:

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

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money) = $9500
- \( r \) is the annual interest rate (decimal) = 8% = 0.08
- \( n \) is the number of times that interest is compounded per year = 365 (since it is compounded daily)
- \( t \) is the number of years the money is invested or borrowed = 5

Now, substituting the values into the formula:

\[
A = 9500 \left(1 + \frac{0.08}{365}\right)^{365 \times 5}
\]

First, calculate \( \frac{0.08}{365} \):

\[
\frac{0.08}{365} \approx 0.0002191781
\]

Then, calculate \( 365 \times 5 = 1825 \).

Now, we plug these values back into the equation:

\[
A = 9500 \left(1 + 0.0002191781\right)^{1825}
\]

Calculating \( 1 + 0.0002191781 \):

\[
1 + 0.0002191781 \approx 1.0002191781
\]

Now raise this to the power of 1825:

\[
\left(1.0002191781\right)^{1825} \approx 1.48985 \text{ (approximately)}
\]

Now, multiply this value by the principal:

\[
A \approx 9500 \times 1.48985 \approx 14154.57
\]

Therefore, the compound amount after 5 years is approximately:

\[
\boxed{14154.57}
\]