Final answer:
To calculate the balance in an account after 3 years with continuous compounding at 9%, use the continuous compounding formula A = Pert with the values P = $20,000, r = 0.09, and t = 3. The final balance is found by calculating e0.09 × 3 and then multiplying this by the principal amount of $20,000.
Step-by-step explanation:
The question asks about calculating the future balance of an investment where the interest is compounded continuously. The formula for continuous compounding is A = Pert, 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), and t is the time the money is invested or borrowed for, in years. In this case, we have:
- P = $20,000 (initial investment)
- r = 9% or 0.09 (interest rate in decimal)
- t = 3 years
To find the balance (A) after 3 years with continuous compounding at 9%, use the formula:
A = 20000 × e0.09 × 3
Calculate the exponent using a calculator to find e0.27 and multiply the result by $20,000. This will give you the balance in the account after 3 years.