Final answer:
To find the time it takes for a principal to earn an interest equal to half of it at 5% simple interest, use the formula Interest = Principal × Rate × Time. In this case, it will take 10 years.
Step-by-step explanation:
To find the length of time it takes for a principal to earn an interest equal to half of it at 5% simple interest, we can use the formula:
Interest = Principal × Rate × Time
Let's assume the principal is P. The interest earned is 0.5P (half of the principal), and the interest rate is 5%. We need to find the time (T).
Thus, we have the equation: 0.5P = P × 0.05 × T
Simplifying the equation gives us: 0.5 = 0.05T
Dividing both sides by 0.05, we get: T = 0.5/0.05 = 10 years
Therefore, it will take 10 years for a principal to earn an interest equal to half of it at a 5% simple interest rate.