Answer :
Ed will have twice as much money as Cindy in approximately 11.22 years.
To determine when Ed will have twice as much money as Cindy, we can set up an equation based on the continuous compound interest formula. The formula for continuous compound interest is given by:
A = P * e^(rt),
where A is the final amount, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.
For Ed:
P = $1000, r = 3% = 0.03, and we want to find t.
For Cindy:
P = $3000, r = 1% = 0.01, and t = t (same as Ed).
We want to find the time when Ed's amount (A_ed) will be twice Cindy's amount (A_cindy):
A_ed = 2 * A_cindy.
Substituting the continuous compound interest formula into the equation, we get:
$1000 * e^(0.03t) = 2 * $3000 * e^(0.01t).
Simplifying the equation, we divide both sides by $3000:
(e^(0.03t))/(e^(0.01t)) = 2/3.
Using the property of exponents, we subtract the exponents:
e^(0.03t - 0.01t) = 2/3.
e^(0.02t) = 2/3.
Taking the natural logarithm (ln) of both sides:
0.02t = ln(2/3).
Solving for t:
t = (ln(2/3))/(0.02).
Using a calculator, we find t ≈ 11.22 years.
Therefore, Ed will have twice as much money as Cindy in approximately 11.22 years.
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