Final answer:
The rate of simple interest that doubles the principal in 6 years is found using the formula for simple interest and is calculated to be 16.67%, which corresponds to option b).
Step-by-step explanation:
To determine the rate of simple interest that leads to a sum doubling over 6 years, we can use the formula of simple interest:
I = P × r × t
Where I is the interest earned, P is the principal amount, r is the rate of interest per year, and t is the time in years.
According to the question, the final amount is double the principal, which means the interest earned equals the principal. This gives us:
P = P × r × 6
Canceling out the principal from both sides, we get:
1 = r × 6
To find the rate r, we divide both sides by 6:
r = 1/6
Converting this to a percentage:
r = (1/6) × 100% = 16.67%
Therefore, the correct answer is b) 16.67%.