To calculate the future value of an investment using the continuous growth formula \( A(t) = Pe^{rt} \), where:
- \( P \) is the principal amount (the initial investment),
- \( r \) is the rate of growth (as a decimal),
- \( t \) is the time in years,
- \( e \) is the base of the natural logarithm (approximately 2.71828).
Given the following values:
- \( P = 10,500 \)
- \( r = 0.0375 \) (3.75% as a decimal)
- \( t = 9 \)
Now, plug these values into the formula:
\[ A(9) = 10,500 \times e^{0.0375 \times 9} \]
First, calculate the exponent:
\[ 0.0375 \times 9 = 0.3375 \]
Now, calculate \( e^{0.3375} \):
\[ e^{0.3375} \approx 1.402248 \]
Now substitute this back into the equation to find \( A(9) \):
\[ A(9) = 10,500 \times 1.402248 \approx 14,781.48 \]
Therefore, the investment amount after 9 years will be approximately $14,781.48.
So the correct response is:
$14,781.48