Simple Interest – Fractional interest and time-rate equality: The simple interest on a sum of money is 1/16 of the principal. The number of years is equal to the rate per cent per annum. Find the rate per cent.

Introduction / Context:
When a question states that the number of years equals the rate per cent per annum, we can set t = r (with r expressed in percent units) and use the simple interest formula to connect the given fraction of principal to r.

Given Data / Assumptions:

• SI = P / 16
• Let rate be r% per annum and time be t years, with t = r

Concept / Approach:
Use SI = P * (r/100) * t and substitute t = r. Then equate to P / 16 and solve for r.

Step-by-Step Solution:
P * (r/100) * r = P / 16r^2 / 100 = 1 / 16 → r^2 = 100 / 16 = 25 / 4r = 5 / 2 = 2.5% (take positive root for a rate)

Verification / Alternative check:
With r = 2.5% and t = 2.5 years, SI = P * 0.025 * 2.5 = P * 0.0625 = P / 16 (matches).

Why Other Options Are Wrong:
3%, 3 1/2%, and 4% correspond to r values whose r^2 / 100 are not 1/16.

Common Pitfalls:
Forgetting that r is in percent while t is in years, or mis-squaring r.

Final Answer:
5/2 %