Q.The true discount on a bill of ₹2,050 due after 6 months is ₹50. Find the rate of interest per annum.

The true discount is the simple interest on the present value, so find the present value first and back out the rate.

Given $F = 2050$, $TD = 50$, $t = \dfrac{6}{12} = 0.5$ year.

Step 1 — Present value:

Step 2 — True discount is simple interest on the present value:

So $r = \dfrac{50}{10} = 5\%$ per annum. …

Charging the true discount on the face value (using 2050 instead of the present value 2000), which gives a slightly wrong rate; …