Answer :
Final answer:
To find the amount in the account after 5 years with continuous compounding at 2% interest rate on [tex]$6000, use the formula A = P e^(rt) where A is the final amount, P is the principal amount, e is the base of the natural logarithm, r is the interest rate, and t is the time.
Explanation:
To calculate the amount in the account after 5 years with continuous compounding, you can use the formula A = P e^(rt), where A is the final amount, P is the principal amount, e is the base of the natural logarithm (approximately 2.71828), r is the interest rate, and t is the time in years.
Plugging in the values: P = $[/tex]6000, r = 2% = 0.02, and t = 5 years, we get A = [tex]$6000 e^(0.025).
Calculating this gives A ≈ $[/tex]6631.81. Therefore, you will have approximately $6631.81 in the account after 5 years.
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