To calculate the amount of money in Tara's account after 15 years with continuous compounding, we can use the formula for continuous compounding:
\[ P(t) = P_0 e^{rt} \]
where:
- \( P(t) \) is the amount in the account at time \( t \),
- \( P_0 \) is the initial principal (the initial amount of money),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time in years,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).
In this case:
- \( P_0 = 2000 \),
- \( r = 0.05 \) (5%),
- \( t = 15 \).
Now we substitute these values into the formula:
\[ P(15) = 2000 e^{0.05 \cdot 15} \]
Calculating the exponent:
\[ 0.05 \cdot 15 = 0.75 \]
Now we calculate \( e^{0.75} \):
\[ e^{0.75} \approx 2.117 \]
Then we can compute \( P(15) \):
\[ P(15) = 2000 \cdot 2.117 \approx 4234.00 \]
So, the amount of money in her account after 15 years is approximately $4,234.00.
The correct answer is B. $4,234.00.
1 answer