Use the compound interest formula for continuous compounding to determine the accumulated balance after the stated period.
A $3,000 deposit in an account with an APR of 6.5% compounded continuously for 4 years.
The formula for calculating the accumulated balance using continuous compounding is:
A = P * e^(rt)
Where:
A = Accumulated balance
P = Principal amount (initial deposit)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time period (in years)
In this case:
P = $3,000
r = 6.5% = 0.065 (converted to decimal form)
t = 4 years
Plugging these values into the formula:
A = $3,000 * e^(0.065 * 4)
Calculating e^(0.065 * 4):
A = $3,000 * e^(0.26)
Using a calculator:
A ≈ $3,000 * 1.295030
A ≈ $3,885.09
Therefore, the accumulated balance after 4 years would be approximately $3,885.09.