What is the true discount on a bill of Rs 2916 that is due 3 years hence, if the rate of interest is 8 percent per annum compounded annually?

Introduction / Context:
This problem uses the concept of true discount in the context of compound interest. The bill amount is due after several years and we need to find the difference between the amount and its present value when the money is discounted at compound interest. That difference is called the true discount. Understanding present value and discounting is very important for financial aptitude questions.

Given Data / Assumptions:
- Amount of the bill (sum due) = Rs 2916.
- Time until the bill is due = 3 years.
- Rate of interest = 8 percent per annum compounded annually.
- We assume standard compound interest formula for calculating present value.
- True discount is defined as amount minus present value.

Concept / Approach:
For compound interest, the future value A after time t years at rate r percent per annum, starting from principal P, is A = P * (1 + r/100)^t. In present value terms, if we know the amount A due after t years, the present value P is A / (1 + r/100)^t. In this question, the amount A is 2916 and we need to find P. Once P is calculated, the true discount TD is simply A − P. We then round to the nearest rupee and compare with the given options.

Step-by-Step Solution:
Step 1: Amount due A = Rs 2916. Step 2: Rate r = 8 percent per annum, time t = 3 years. Step 3: Present value P is given by P = A / (1 + r/100)^t. Step 4: Compute the compound factor: (1 + 8/100)^3 = 1.08^3. Step 5: Calculate 1.08^3 = 1.08 * 1.08 * 1.08 = 1.259712 (approximately). Step 6: Present value P ≈ 2916 / 1.259712 ≈ 2314.82 rupees. Step 7: True discount TD = A − P ≈ 2916 − 2314.82 ≈ 601.18 rupees. Step 8: Rounded to the nearest rupee, the true discount is approximately Rs 601.

Verification / Alternative check:
We can check the closeness by reversing the process. If the present value is about Rs 2315 at 8 percent compound interest for 3 years, future value is 2315 * 1.08^3 ≈ 2315 * 1.259712 ≈ 2916 (within a rounding difference). This confirms that the present value and the computed true discount of roughly Rs 601 are correct for the given amount and interest rate.

Why Other Options Are Wrong:
Option Rs 600: Slightly smaller than the correct discount and does not match the precise calculation using the compound interest formula.
Option Rs 602 and Rs 603: Slightly larger than the accurate rounded value obtained from the calculation and therefore not correct when using standard rounding rules.

Common Pitfalls:
Some learners mistakenly apply simple interest formulas in compound interest questions or attempt to treat the yearly interest linearly. Others may confuse true discount with simple interest on the present value. It is important to use the proper compound factor (1 + r/100)^t, compute present value correctly, and then subtract from the amount to obtain the true discount.

Final Answer:
The true discount on the bill is approximately Rs 601.