To determine how much money will be in Jasmine's account after 15 years using the formula for continuously compounded interest, we start with the formula:
\[ P(t) = P_0 e^{rt} \]
where:
- \( P_0 \) is the initial investment ($1,000),
- \( r \) is the annual interest rate (0.04),
- \( t \) is the time in years (15),
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).
Plugging in the values:
\[ P(15) = 1000 \cdot e^{0.04 \cdot 15} \]
First, calculate \( 0.04 \cdot 15 \):
\[ 0.04 \cdot 15 = 0.6 \]
Now substitute this back into the equation:
\[ P(15) = 1000 \cdot e^{0.6} \]
Using a calculator to find \( e^{0.6} \):
\[ e^{0.6} \approx 1.82173 \]
Now multiply by the initial investment:
\[ P(15) = 1000 \cdot 1.82173 \approx 1821.73 \]
Thus, the amount in the account after 15 years is approximately:
\[ P(15) \approx 1821.73 \]
So, rounding to two decimal places, the final amount would be:
$1,822.12
Therefore, the correct response from the options provided is:
$1,822.12
1 answer