Questions: A certificate of deposit has a principal of P dollars and an annual percentage rate of r (expressed as a decimal) compounded n times per year. The balance A in the account is given by [ A=Pleft(1+fracrnright)^N ] where N is the number of compoundings. Use a graphing utility to find the balance in the account. (Round your answer to the nearest cent.) [ P= 5000, r=5 %, n=365, N=1800 ] [ A= ]

Solution Steps

To find the balance in the account, we need to use the given formula for compound interest. We will substitute the given values for \( P \), \( r \), \( n \), and \( N \) into the formula and compute the result.

1. Substitute the given values into the formula:
   • \( P = 5000 \)
   • \( r = 0.05 \) (since 5% as a decimal is 0.05)
   • \( n = 365 \)
   • \( N = 1800 \)
2. Compute the balance \( A \) using the formula: \[ A = P \left(1 + \frac{r}{n}\right)^N \]
3. Round the result to the nearest cent.

We start with the formula for the balance \( A \) in the account given by:

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

Substituting the given values:

• \( P = 5000 \)
• \( r = 0.05 \)
• \( n = 365 \)
• \( N = 1800 \)

Now we compute \( A \):

\[ A = 5000 \left(1 + \frac{0.05}{365}\right)^{1800} \]

Calculating \( \frac{0.05}{365} \):

\[ \frac{0.05}{365} \approx 0.0001369863 \]

Thus, we have:

\[ A = 5000 \left(1 + 0.0001369863\right)^{1800} \]

Calculating \( A \):

\[ A \approx 5000 \left(1.0001369863\right)^{1800} \approx 6398.069906161905 \]

Rounding \( A \) to the nearest cent gives:

\[ A_{\text{rounded}} = 6398.07 \]

Final Answer