Answer:
It seems you're looking at a math problem related to compound interest. The formula to calculate the final amount \( A \) in an account with continuous compounding is given by the formula:
[tex]\[ A = Pe^{rt} \][/tex]
where:
- \( P \) is the principal amount (the initial amount of money),
- \( r \) is the annual interest rate (expressed as a 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).
Given your problem:
- [tex]\( P = $6000 \)[/tex],
- [tex]\( r = 8\% = 0.08 \)[/tex],
- [tex]\( t = 15 \)[/tex] years.
Let's calculate the amount of money you will have in the account after 15 years.
After 15 years, with an 8% interest rate compounded continuously, you will have approximately $19,920.70 in the account.
Step-by-step explanation:
