Final answer:
The correct option is a. It will become sixteen times its original value. Therefore, if the principal is doubled, the simple interest will also be double the principal.
Step-by-step explanation:
If the principal is doubled at r% per annum in t years, the simple interest (SI) can be calculated using the formula Interest = Principal × rate × time. Because we are given that the principal doubles over t years, the accumulated simple interest during this time is equal to the principal itself. Therefore, if the principal is doubled, the simple interest will also be double the principal.
The correct option is a. It will become sixteen times its original value.
To understand why, we can use the formula for Simple Interest (SI):
SI = P * r * t
Where P is the principal amount, r is the rate of interest, and t is the time in years.
According to the question, if the principal is doubled, it means P becomes 2P. So, the new SI is:
New SI = (2P) * r * t = 2 * (P * r * t) = 2 * SI = 16 * P
Therefore, the SI will become sixteen times the principal.