if 8000 is invested in a long-term trust fund with an interest rate of 5% compounded continuously what is the amount of money in the account after 15 years?
amount = 8000 * e^(.05 * t)
Thanks
To calculate the amount of money in an account after a certain time period with continuous compounding interest, we can use the formula:
A = P * e^(rt)
Where:
A = the amount of money in the account after the specified time period
P = the principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = the interest rate (in decimal form)
t = the time period (in years)
In this case:
P = $8000
r = 5% = 0.05 (in decimal form)
t = 15 years
Plugging in these values into the formula:
A = $8000 * e^(0.05 * 15)
Now, let's calculate this using Python:
```python
import math
P = 8000
r = 0.05
t = 15
A = P * math.exp(r * t)
A
```
By running this code, we find that the amount of money in the account after 15 years is approximately $19,538.94.