An initial investment of $5000 doubles in value in 11 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.
A)2.7%
B)3.2%
C)11%
D)6.3%
E)100%

Question

Quizplus · Accepted Answer

Using the formula for continuous compounding:

A = Pe^(rt)

Where:

A = final amount = $10,000
P = initial amount = $5000
r = interest rate
t = time in years = 11

Substituting the known values:

$10,000 = $5000e^(11r)

Dividing by $5000:

2 = e^(11r)

Taking the natural logarithm of both sides:

ln(2) = 11r

Solving for r:

r = ln(2)/11 ≈ 0.0633

Converting to a percentage and rounding to the nearest tenth:

r ≈ 6.3%

Therefore, the answer is (D) 6.3%.

An Initial Investment of $5000 Doubles in Value in 11