An initial investment of $1240 is appreciated for 17 years in an account that earns 8% interest, compounded continuously. Find the amount of money in the account at the end of the period.
amount=1240(1+.08)^17
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1240(1+.08)^17
To find the amount of money in the account at the end of the period, we can use the formula for continuous compound interest:
A = P * e ^(rt)
Where:
A is the amount of money in the account at the end of the period
P is the initial investment
e is Euler's number, approximately equal to 2.71828
r is the interest rate
t is the time in years
In this case, P = $1240, r = 0.08 (8% expressed as a decimal), and t = 17 years. Plugging these values into the formula, we get:
A = 1240 * e ^(0.08 * 17)
To evaluate this expression, we need to calculate e ^(0.08 * 17). Here's how you can do that:
1. Multiply 0.08 and 17: 0.08 * 17 = 1.36
2. Raise e to the power of 1.36: e^(1.36)
Now, since e is a mathematical constant, you can use the approximate value e = 2.71828. To calculate e ^(1.36), follow these steps:
1. Raise 2.71828 to the power of 1.36: 2.71828^(1.36)
By evaluating this expression, we find that e ^(1.36) is approximately equal to 3.8947.
Now, substitute this value back into the original equation to find the amount of money in the account at the end of the period:
A = 1240 * 3.8947
Evaluating this expression, we find that the amount of money in the account at the end of the 17-year period is approximately $4,823.34.