Q.A person buys 50 debentures of face value ₹100 each, at a market price of ₹96 per debenture, paying a brokerage of ₹1 per debenture. The debentures carry 12% annual interest. Find

Find the effective buying price per debenture (market price plus brokerage), the total investment, the annual interest income (on face value), and then the rate of return.

Step 1 — Find the effective buying price per debenture. $\text{Effective Buying Price} = \text{Market Price}+\text{Brokerage} = 96+1=97$.

Step 2 — Find the total investment. $\text{Total Investment} = 50\times97 = 4{,}850$.

Step 3 — Find the annual interest income (on face value, not market/buying price). $\text{Annual Interest} = 50\times100\times\dfrac{12}{100} = 5000\times0.12=600$.

Step 4 — Find the rate of return.

$\text{Rate of Return} = \dfrac{\text{Annual Income}}{\text{Investment}}\times100 = \dfrac{600}{4850}\times100 \approx 12.37\%$ …

The qualitative check — discount-purchase pushes return above the nominal rate, premium-purchase pulls it below — is a fast way to sanity-ch …

Computing the annual interest on the ₹97 buying price instead of the ₹100 face value is a frequent error — interest (like dividend) is always a perc …