Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. How much money invested at 5% compounded continuously for 3 years will result in $820?
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In order to find out how much money needs to be invested at 5% compounded continuously for 3 years to result in $820, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A is the final amount
P is the principal amount (the initial investment)
e is Euler's number (approximately equal to 2.71828)
r is the interest rate (in decimal form)
t is the time (in years)
In this case, we want to find P, so we can rearrange the formula:
P = A / e^(rt)
Now let's substitute the given values into the formula:
A = $820
r = 5% = 0.05 (since it's already in decimal form)
t = 3
P = $820 / e^(0.05*3)
P = $820 / e^(0.15)
Using a calculator, we can calculate e^(0.15) ≈ 1.16183.
P = $820 / 1.16183
P ≈ $705.72
Therefore, approximately $705.72 should be invested at 5% compounded continuously for 3 years in order to result in $820.