Final answer:
Using the formula A = Pe^{rt} for continuous compounding interest, with $4000 deposited at 6% interest for 10 years, the account balance will grow to approximately $7,238.66.
Step-by-step explanation:
To determine how much money will be in an account after a certain period with continuous compounding interest, we use the formula A = Pert where:
- P is the principal amount (the initial amount of money)
- e is the base of the natural logarithm (approximately 2.71828)
- r is the annual interest rate (in decimal form)
- t is the time in years
For a $4000 deposit at 6% interest compounded continuously for 10 years, the calculation is:
A = $4000e(0.06×10)
This leads to:
A = $4000e0.6
By calculating this expression, we find the amount of money in the account after 10 years.
After 10 years, the amount of money in the account would be approximately $7,238.66.