Simple Interest – Interest equals a small fraction of principal: The simple interest on a sum of money is 1/144 of the principal. The number of years is equal to the rate per cent per annum. What is the rate per cent per annum?

Introduction / Context:
Problems that state 'years equals rate (in % per annum)' can be solved by expressing both in a single variable and using the simple interest formula.

Given Data / Assumptions:

• SI = P / 144
• Let the rate be r% per annum and time be t years with t = r

Concept / Approach:
Simple interest: SI = P * (r/100) * t. Substitute t = r and equate to P/144 to solve for r.

Step-by-Step Solution:
P * (r/100) * r = P / 144r^2 / 100 = 1 / 144 → r^2 = 100 / 144 = 25 / 36r = 5 / 6 (take positive root for a rate)

Verification / Alternative check:
With r = 5/6% and t = 5/6 years, SI = P * (5/6)/100 * (5/6) = P * 25 / 3600 = P / 144 (matches).

Why Other Options Are Wrong:
3/5%, 1/6%, 7/6% do not satisfy r^2 / 100 = 1/144.

Common Pitfalls:
Interpreting r as a decimal rather than percent in t = r, or taking the negative square root.

Final Answer:
5/6%