Answer :
Answer:
To calculate the value of the account after \( t \) years, we can use the formula for compound interest:
\[ A = P \times \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after \( t \) years, including interest.
- \( P \) is the principal amount (the initial investment).
- \( r \) is the annual interest rate (in decimal).
- \( n \) is the number of times interest is compounded per year.
- \( t \) is the time the money is invested for, in years.
Given \( P = 7400 \), \( r = 0.068 \), and since it's compounded daily, \( n = 365 \):
\[ A = 7400 \times \left(1 + \frac{0.068}{365}\right)^{365t} \]
So, the function for the value of the account after \( t \) years would be:
\[ A(t) = 7400 \times \left(1 + \frac{0.068}{365}\right)^{365t} \]
To determine the Annual Percentage Yield (APY), we can use the formula:
\[ APY = \left(1 + \frac{r}{n}\right)^n - 1 \]
Given \( r = 0.068 \) and \( n = 365 \):
\[ APY = \left(1 + \frac{0.068}{365}\right)^{365} - 1 \]
Let me calculate those for you.The function for the value of the account after \( t \) years is:
\[ A(t) = 7400 \times \left(1 + \frac{0.068}{365}\right)^{365t} \]
And the Annual Percentage Yield (APY) is approximately 7.03%.
