Answer:
To find the amount in the account after five years with continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = Amount in the account after time t
P = Initial principal (initial amount invested)
e = Euler's number (approximately 2.71828)
r = Interest rate per year (as a decimal)
t = Time in years
Given:
Initial amount (P) = $2500
Interest rate (r) = 6% per year (0.06 as a decimal)
Time (t) = 5 years
Plugging in the values into the formula:
A = 2500 * e^(0.06 * 5)
Calculating the exponent:
A = 2500 * e^(0.3)
Using a calculator or a computer, we can evaluate e^(0.3) to be approximately 1.34986.
Calculating the final amount:
A = 2500 * 1.34986
A ≈ $3374.65
Therefore, the amount in the account after five years, with continuous compounding, is approximately $3374.65
Step-by-step explanation: