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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amount = 2000(e^(3(.051)) ?
i got 9236.35
To solve this problem, we can use the formula for continuously compounded interest:
A = P * e^(r*t)
Where:
A = the total amount after t years
P = the initial principal (the amount you invest)
r = the annual interest rate (in decimal form)
t = the time in years
e = Euler's number, approximately 2.71828
Using the formula, we can substitute the given values:
P = $2000
r = 5.1% = 0.051 (in decimal form)
t = 3 years
A = 2000 * e^(0.051*3)
Now, let's calculate the result step by step:
Step 1: Calculate the exponent
0.051 * 3 = 0.153
Step 2: Calculate the exponent of e
e^(0.051*3) ≈ 1.156517
Step 3: Multiply the principal by the result
2000 * 1.156517 ≈ 2313.03
After rounding to the nearest dollar, you will have approximately $2313 in the account after 3 years.