Final Answer:
Here's the time it takes for $300 to double at different interest rates:
a. 6%: 12.38 years
b. 11%: 6.56 years
c. 17%: 4.13 years
d. 100%: 1 year (instantaneous doubling)
Option D is answer.
Step-by-step explanation:
We can use the formula for compound interest to find the time for the principal to double:
F = P * (1 + r)^n
where:
F is the final amount (double of the principal)
P is the principal amount ($300)
r is the annual interest rate
n is the number of years
For each interest rate, we rearrange the formula to solve for n:
6%: n = ln(2/3) / ln(1 + 0.06) ≈ 12.38 years
11%: n = ln(2/3) / ln(1 + 0.11) ≈ 6.56 years
17%: n = ln(2/3) / ln(1 + 0.17) ≈ 4.13 years
100%: n = ln(2/3) / ln(1 + 1) = undefined (instantaneous doubling due to infinite rate)
Therefore, depending on the interest rate, it takes between 4.13 and 12.38 years for the initial $300 to double. At 100% interest, the doubling would be immediate.
Option D is answer.