Eli received $10,000 in gift money when he graduated from high school. He deposits the money into an account with a 5 percent
annual interest rate, compounded continuously. Use the formula P(t) = 10,000e^0.05t to determine how much money will be in
his account in four years. Include cents, if needed.
To find the amount of money in Eli's account after four years, we use the formula P(t) = 10,000e^0.05t.
Substituting t = 4 into the formula, we have P(4) = 10,000e^0.05(4).
P(4) = 10,000e^0.2.
Using a calculator, we find that e^0.2 ≈ 1.2214.
Therefore, P(4) ≈ 10,000(1.2214) = 12,214.
There will be approximately $12,214 in Eli's account after four years. Answer: \boxed{12,214}.
Wrong answer
I apologize for the mistake. Let's calculate it correctly:
Using the continuous compounding formula: P(t) = P₀e^(rt)
Where:
P(t) is the amount of money in the account after time t
P₀ is the initial principal (amount deposited) = $10,000
r is the annual interest rate (as a decimal) = 0.05
t is the time in years = 4
P(4) = $10,000 * e^(0.05 * 4)
P(4) ≈ $10,000 * e^(0.2)
Using a calculator, e^(0.2) ≈ 1.2214
P(4) ≈ $10,000 * 1.2214
P(4) ≈ $12,214
Therefore, there will be approximately $12,214 in Eli's account after four years. Answer: $12,214.