Find rate from present worth: At simple interest, the present worth of $1245 due in 15 months is $1200. What is the annual rate of interest?

Introduction / Context:
The link between present worth P, future sum S, time t in years, and annual simple-interest rate r is S = P * (1 + r t). Knowing P, S, and t, we can directly solve for r as a simple proportion, then express it per annum as a percentage.

Given Data / Assumptions:

• S = $1245 (due amount).
• P = $1200 (present worth).
• t = 15 months = 1.25 years.

Concept / Approach:
Use S = P(1 + r t) ⇒ r = (S/P − 1) / t. Substitute numerical values, being careful to convert months to years, and finally multiply by 100 to get percent per annum.

Step-by-Step Solution:

Verification / Alternative check:
Check forward: P(1 + r t) = 1200 * (1 + 0.03 * 1.25) = 1200 * 1.0375 = 1245, consistent.

Why Other Options Are Wrong:

• 4%, 5%, 6%: Do not satisfy the proportional relation at 1.25 years.

Common Pitfalls:
Forgetting to convert months to years or mixing the bases (using discount formulas instead of simple-interest growth).

Final Answer:
3%