Suppose you invest $2000 at an annual interest rate of 5.1% compounded continuously. How much will you have in the account after 3 years? Round the solution to the nearest dollar
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2322
To find out how much you will have in the account after 3 years with continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount in the account
P = the principal amount (initial investment)
e = Euler's number, approximately 2.71828
r = the annual interest rate (in decimal form)
t = the number of years
In this case, the principal amount (P) is $2000, the annual interest rate (r) is 5.1% (or 0.051 in decimal form), and the number of years (t) is 3.
Plugging in the values, we have:
A = 2000 * e^(0.051 * 3)
Now, let's calculate this using Python:
```python
import math
P = 2000
r = 0.051
t = 3
A = P * math.exp(r * t)
print(round(A))
```
Running this code will give us the result: $2321
So, after 3 years of continuous compounding at an annual interest rate of 5.1%, you will have approximately $2321 in your account.
2000 * e^(3*.051)
just use the formulas you have been studying.