Final answer:
Using the continuous compounding formula A = Pert, with a principal of $4000, a rate of 6%, and a time period of 10 years, the final amount in the account would be approximately $7,288.48.
Step-by-step explanation:
To calculate the amount of money you will have in an account after 10 years when it compounds continuously at 6% interest, you use the continuous compounding formula A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), t is the time the money is invested for in years, and e is the base of the natural logarithm (approximately equal to 2.71828).
In this scenario, you deposit $4000 at an interest rate of 6% (0.06 as a decimal), compounded continuously, for 10 years. The formula simplifies to:
A = 4000 × e(0.06 × 10)
Using a calculator, you get:
A = 4000 × e0.6
A = 4000 × 1.822118800
The amount after 10 years is approximately $7,288.48.