Aidan has $7565 in his checking account. He invests $5000 of it in an account that earns 3.5% intersest compounded continuously. What is the total amount of his investment after 3 years?
5000e^(.035*3) = 5553.55
thanks!
To find the total amount of Aidan's investment after 3 years, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount
P = the principal amount (initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (expressed as a decimal)
t = the number of years
Given that Aidan invests $5000 at an interest rate of 3.5% compounded continuously for 3 years, we can plug these values into the formula:
P = $5000
r = 3.5% = 0.035 (as a decimal)
t = 3 years
A = $5000 * e^(0.035 * 3)
Now let's calculate the value of e^(0.035 * 3) using a calculator:
e^(0.035 * 3) ≈ 1.036563
Substituting this value back into the formula:
A = $5000 * 1.036563
Calculating this expression:
A ≈ $5,182.82
Therefore, the total amount of Aidan's investment after 3 years is approximately $5,182.82.
To find the total amount of Aidan's investment after 3 years, we can use the formula for compound interest:
A = P * e^(rt)
Where:
A = Total amount after time t
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (expressed as a decimal)
t = Time (in years)
In this case, Aidan invests $5000, so P = 5000. The annual interest rate is 3.5% or 0.035 as a decimal, so r = 0.035. The time is 3 years, so t = 3.
Plug these values into the formula:
A = 5000 * e^(0.035 * 3)
To calculate this using a calculator, follow these steps:
1. Multiply 0.035 by 3: 0.035 * 3 = 0.105
2. Calculate the value of e^(0.105) on your calculator.
3. Multiply the result by 5000: 5000 * result
The final result will give you the total amount of Aidan's investment after 3 years.