A woman wants to give ₹ 32,800 to her two grandchildren aged 17 years and 18 years. They must get equal amounts when they are 20 years at 5% p.a. compound interest. Find the present share of the younger grandchild.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹ 16,000
Each share grows at 5% compound interest until its owner is 20, and the two grown amounts must be equal. The younger grandchild (17) has 3 years to reach 20 and the elder (18) has 2 years.
Comparing the two shares (younger’s share \(x\), elder’s \(y\)):
\(x(1.05)^3=y(1.05)^2\)
\(y=1.05x\)
Finding x (the two shares make up ₹ 32,800):
\(x+1.05x=32800\)
\(2.05x=32800\)
\(x=16000\), so the younger grandchild’s share is ₹ 16,000 (and the elder’s ₹ 16,800)