Compound Interest — ₹ 8,448 is to be divided between A (age 18) and B (age 19) so that if their present shares are invested at 6.25% per annum compounded annually, they will receive equal amounts when each turns 21 years old. What is A’s present share?

Introduction / Context:
This is a present-worth allocation under compound interest. Two people receive money today but will let it grow for different numbers of years before comparing outcomes at a common target age. Because the annual rate is the same for both, we can relate their present shares by requiring equal future amounts on their respective “turning-21” dates.

Given Data / Assumptions:

• Total to divide now = ₹ 8,448.
• A is 18, so money grows for 3 years (to age 21).
• B is 19, so money grows for 2 years (to age 21).
• Rate r = 6.25% = 0.0625 per annum, compounded annually. Growth factor g = 1 + r = 1.0625.

Concept / Approach:
Let present shares be A0 for A and B0 for B. Equal future amounts at age 21 mean A0 * g^3 = B0 * g^2. Thus A0 / B0 = g^(2−3) = g^(−1) = 1 / g. Therefore A0 : B0 = 1 : g = 16 : 17, using g = 17/16.

Step-by-Step Solution:
Ratio A0 : B0 = 16 : 17Total parts = 16 + 17 = 33Value per part = 8,448 / 33 = 256A0 = 16 × 256 = ₹ 4,096B0 = 17 × 256 = ₹ 4,352

Verification / Alternative check:
Future amounts at 21: A's future = 4,096 * (1.0625)^3; B's future = 4,352 * (1.0625)^2. Since (1.0625)^3 / (1.0625)^2 = 1.0625, and A0/B0 = 1/1.0625, both futures match exactly.

Why Other Options Are Wrong:
₹ 4,352 is B's present share, not A's. ₹ 4,225 and ₹ 4,180 break the 16:17 ratio. ₹ 4,000 also fails to satisfy the equality of future amounts at the given rate.

Common Pitfalls:
Using simple interest instead of compound growth; forgetting that A grows for 3 years while B grows for only 2; or dividing the total equally without adjusting for time.

Final Answer:
₹ 4,096