Complete the table to determine the balance A for $10,000 invested at rate r = 4% for t years, compounded continuously. (Round your answers to two decimal places.)
Question
Complete the table to determine the balance A for $10,000 invested at rate r = 4% for t years, compounded continuously. (Round your answers to two decimal places.)
Solution
To calculate the balance A for $10,000 invested at rate r = 4% for t years, compounded continuously, we use the formula for continuous compounding:
A = P * e^(rt)
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- t is the time the money is invested for in years.
- e is Euler's number (approx. 2.71828).
Given that P = $10,000 and r = 4% = 0.04, we can substitute these values into the formula to get:
A = 10000 * e^(0.04t)
Now, you can substitute the different values of t (in years) into this formula to get the corresponding values of A (the balance after t years). Remember to round your answers to two decimal places.
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