Mutual debts settled immediately using present worth M owes N ₹ 3,146 payable 1.5 years hence. N owes M ₹ 2,889 payable 6 months hence. If they settle accounts now at a simple interest rate of 14% per annum, who pays whom and how much?

Introduction / Context:When two parties owe each other different sums at different future dates, a fair immediate settlement requires discounting both future amounts to their present worth at the agreed simple interest rate, then netting the present values.

Given Data / Assumptions:

• M owes N: ₹ 3,146 due in 1.5 years.
• N owes M: ₹ 2,889 due in 0.5 year.
• Simple interest r = 14% per annum.

Concept / Approach:Present worth PW = S / (1 + r * t) for each obligation. After computing PW(M owes) and PW(N owes), the net payer is the one whose PW obligation is larger in the opposite direction; the difference is the immediate cash settlement.

Step-by-Step Solution:PW(M owes) = 3,146 / (1 + 0.14 * 1.5) = 3,146 / 1.21 = ₹ 2,600.PW(N owes) = 2,889 / (1 + 0.14 * 0.5) = 2,889 / 1.07 = ₹ 2,700.Net PW = ₹ 2,700 − ₹ 2,600 = ₹ 100 in favor of M.Therefore, N should pay M ₹ 100 now.

Verification / Alternative check:Forward check: If M receives ₹ 100 now and interest accrues appropriately, at their respective due dates the balances would offset exactly, confirming fairness of the settlement.

Why Other Options Are Wrong:Amounts other than ₹ 100 do not match the exact difference in present worths; reversing payer directions contradicts the computed signs.

Common Pitfalls:Using simple interest to grow instead of discount to present, or mixing due periods. Always convert both amounts to the same “now” position before netting.

Final Answer:N should pay ₹ 100