If $9,000 is invested at an annual rate of 11% per year compounded monthly, the future value S at any time t (in months) is given by . How long does it take for the investment to double? Round your answer to one decimal place.
A) 91.2 months
B) 14.8 months
C) 76.0 months
D) 92.2 months
E) 68.7 months

Question

If $9,000 is invested at an annual rate of 11% per year compounded monthly, the future value S at any time t (in months) is given by  . How long does it take for the investment to double? Round your answer to one decimal place. ​
A) 91.2 months 
B) 14.8 months 
C) 76.0 months 
D) 92.2 months 
E) 68.7 months

Quizplus · Accepted Answer

We need to find the time it takes for the investment to double, which means we need to solve for the value of t in the equation:

$2S = 9,000(1 + 0.11/12)^t$

Divide both sides by 9,000:

$2(1 + 0.11/12)^t = 2$

Simplify:

$(1.00917)^t = 2$

Take the natural log of both sides:

$t\ln(1.00917) = \ln(2)$

Divide both sides by ln(1.00917):

$t = \frac{\ln(2)}{\ln(1.00917)} \approx 76.0$ months

Round to one decimal place: 76.0 months.

Hence, the answer is C.

If $9,000 Is Invested at an Annual Rate of 11