Simple Interest — Symbolic condition where rate% equals time: On a certain principal, the simple interest equals 9/16 of the principal. If the numerical values of rate percent per annum and time in years are equal, what is the time?

Introduction / Context:Symbolic SI problems test fluency with variables and percent conversion. When the rate in percent and the time (in years) are equal numerically, the product r * t must be formed carefully using r in decimal form (percent divided by 100).

Given Data / Assumptions:

• SI = (9/16) * P
• Let rate percent = time in years = n (so r = n/100, t = n)

Concept / Approach:Under SI: SI = P * r * t = P * (n/100) * n = P * n^2 / 100. Equate to (9/16) * P and solve for n. Cancel P > 0 from both sides.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Other durations do not satisfy n^2 = 56.25.

Common Pitfalls:

• Using n (percent) directly without dividing by 100.

Final Answer:7 1/2 years.