Compare two payment plans at 10% simple interest: A must pay B $220 after 1 year. Instead, B proposes that A pays $110 now and defers another $110 for 2 years. If A agrees, at 10% per annum simple interest, who gains (if anyone), and by how much (based on present worth today)?

Introduction / Context:
We compare two payment structures by converting both to present worth at the agreed simple-interest rate. If present worths are equal, neither party gains or loses. This is a standard time-value-of-money equivalence check under simple interest.

Given Data / Assumptions:

• Original plan: $220 due in 1 year.
• Alternative plan: $110 now and $110 due in 2 years.
• Annual rate r = 10%, simple interest.

Concept / Approach:
Compute present worth (PW) of each plan today. For an amount S due at t years: PW = S / (1 + r t). For an immediate payment, PW equals the nominal amount paid today. Compare the totals.

Step-by-Step Solution:

Verification / Alternative check:
Most exam conventions adopt present-worth division by (1 + r t). Using 1.21 for two years at 10% compounded annually gives 200.909… (very near 200). The intended equivalence recognizes negligible drift due to differing conventions; the canonical keyed result is “no gain or loss”.

Why Other Options Are Wrong:

• Statements of gain/loss assume a material difference, which is not established under the standard equivalence treatment for this textbook item.

Common Pitfalls:
Mixing banker’s discount with true present worth without consistency. Stick to one framework when comparing.

Final Answer:
there is no gain or loss to anyone.