Find (i) the present worth and (ii) the true discount of a bill of Rs. 2420 due after 2 years at 10% compound interest per annum.

Introduction / Context:
With compound interest, present worth is found by discounting the face value by (1 + r)^n. True discount equals the difference between face value and present worth.

Given Data / Assumptions:

• F = 2420
• r = 10% compounded
• n = 2 years

Concept / Approach:
P = F / (1 + r)^n. TD = F − P.

Step-by-Step Solution:
(1 + r)^n = 1.1^2 = 1.21. P = 2420 / 1.21 = 2000. TD = 2420 − 2000 = 420.

Verification / Alternative check:
2000 grows to 2000 * 1.21 = 2420 in 2 years at 10%, so the calculation is exact.

Why Other Options Are Wrong:
All other pairs do not correspond to discounting at 10% compounded for 2 years.

Common Pitfalls:
Using simple interest discounting; or incorrectly computing 1.1^2; or swapping present worth and discount values.

Final Answer:
Rs. 2000, Rs. 420