Suppose that interest on money in the bank accumulates at an annual rate of 6% per year compounded continuously. If you deposit $3000 in the account today, how much will it be worth 20 years from now?
(Hint: First find the equation that represents the balance B = B(t) in the
account at time t years.)
To find the balance B in the account at time t years, we can use the formula for continuous compound interest:
B = Pe^(rt)
Where:
B = balance in the account at time t
P = initial deposit amount
r = annual interest rate
t = time in years
e = Euler's number (approximately 2.71828)
Given:
P = $3000
r = 6% = 0.06
t = 20 years
Plug in the values:
B = 3000 * e^(0.06*20)
B = 3000 * e^(1.2)
B ≈ 3000 * 3.32012
B ≈ $9960.36
Therefore, the account will be worth approximately $9960.36 after 20 years.