How long will it take an investment of $9,000 to double if the investment earns interest at the rate of 9% / year compounded monthly?
A) 7.5 year(s)
B) 7.8 year(s)
C) 7.7 year(s)
D) 8.0 year(s)

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the ending balance (in this case, $18,000)
P = the principal (in this case, $9,000)
r = the annual interest rate (9%)
n = the number of times the interest is compounded per year (12, since it is compounded monthly)
t = the time (in years) the money is invested

We want to solve for t, so we can rearrange the equation as follows:

t = (log(A/P)) / (n * log(1 + r/n))

Plugging in the numbers, we get:

t = (log(2) / log(1 + 0.09/12)) / 12
t ≈ 7.7 years

Therefore, it will take approximately 7.7 years for the investment to double. So, the correct answer is C).

How Long Will It Take an Investment of $9,000 to Double