Present worth at two maturities (same rate): A bill due in 4 years is worth $575 now, but if it were due in 2 years 6 months it would be worth $620 now. Assuming simple interest, find the sum due on the bill (face value).

Introduction / Context:
Two present-worth figures are quoted for the same future bill but with different times to maturity. Under simple interest, present worth PW and sum due S satisfy PW = S / (1 + r t). By forming a ratio of the two given PWs we eliminate S and solve for the rate r, then back-substitute to obtain S.

Given Data / Assumptions:

• PW₁ = 575 at t₁ = 4 years.
• PW₂ = 620 at t₂ = 2.5 years.
• Simple interest at a constant annual rate r.

Concept / Approach:
Use PW = S / (1 + r t). Then 620/575 = (1 + r*4) / (1 + r*2.5). Solve for r, then compute S from either PW equation. This approach avoids guessing and uses only proportional reasoning plus one substitution.

Step-by-Step Solution:

Verification / Alternative check:
Check PW using t₁ = 4: PW = 713 / (1 + 0.24) = 713 / 1.24 = 575 (matches).

Why Other Options Are Wrong:

• $695, $725, others: Do not satisfy both present-worth equations at a single rate.

Common Pitfalls:
Mistaking compound for simple interest or mixing the two PWs without eliminating S first.

Final Answer:
$ 713