Suppose you invest $400 at an annual interest rate of 7.6% compounded continuously. How much will you have in the account after 1.5 years. Round to the nearest dollar.
Hello, I also have this question, but I don't know the answer.
To calculate the amount after 1.5 years with continuous compounding, we can use the formula:
A = P*e^(rt)
Where:
A = final amount
P = initial principal
e = Euler's number (approximately 2.71828)
r = annual interest rate as a decimal
t = time in years
In this case:
P = $400
r = 7.6% or 0.076
t = 1.5 years
Substituting these values into the formula:
A = $400 * e^(0.076 * 1.5)
Using a calculator, we can find:
A ≈ $400 * 2.200394733
A ≈ $880.16
So, you would have approximately $880 in the account after 1.5 years with continuous compounding.
To find out how much you will have in the account after 1.5 years with continuous compounding, you can use the formula:
A = P * e^(rt)
Where:
A is the final amount in the account
P is the initial investment (principal)
e is the base of the natural logarithm (approximately 2.718)
r is the annual interest rate
t is the time in years
In this case, the initial investment (P) is $400, the annual interest rate (r) is 7.6% (or 0.076 in decimal form), and the time (t) is 1.5 years.
Plugging these values into the formula, we get:
A = 400 * e^(0.076 * 1.5)
Now, let's calculate this using a calculator or a programming language that has the exponential function built-in, such as Python:
```python
import math
P = 400
r = 0.076
t = 1.5
A = P * math.exp(r * t)
```
Evaluating this expression:
A ≈ 458.52
Therefore, you would have approximately $458.52 in the account after 1.5 years with continuous compounding.
a = A e^rt
a = 400 e^.076(1.5)
a = 448.