How long will it take for $600 to double if it is invested at 9% annual interest compounded 12 times a year?
A) It will take approximately 11.1 years.
B) It will take approximately 8.8 years.
C) It will take approximately 7.7 years.
D) It will take approximately 7.4 years.
E) It will take approximately 8.4 years.

Question

Quizplus · Accepted Answer

We can use the formula for compound interest, A=P(1+r/n)^(nt), where A is the final amount, P is the initial amount, r is the annual interest rate, n is the number of times compounded per year, and t is the time in years. We want to find t when A=2P and substitute the given values.

2P = 600(1+0.09/12)^(12t)
2 = (1.0075)^(12t)
log(2) = log(1.0075)^(12t)
log(2) = 12t*log(1.0075)
t = log(2)/(12*log(1.0075))
t ≈ 7.7 years

Therefore, it will take approximately 7.7 years for $600 to double if it is invested at 9% annual interest compounded 12 times a year. The answer is choice C.

How Long Will It Take for $600 to Double If