Aman invested ₹(P + 3000) for 3 years at 8% simple interest. Anuj invested an amount of ₹P for 2 years at 12% compound interest and received the same amount of interest as Aman received. Find the amount that is invested by Anuj.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹50,000
Simple interest is \(\displaystyle\frac{P\times R\times T}{100}\); compound interest for 2 years is \(P\left(1+\frac{R}{100}\right)^2-P\). The question says the two interests are equal.
Aman’s simple interest (8% for 3 years on \(P+3000\)):
\(\displaystyle (P+3000)\times\frac{8\times3}{100}=0.24P+720\)
Anuj’s compound interest (12% for 2 years on \(P\)):
\(P\times(1.12)^2-P=1.2544P-P=0.2544P\)
Equating the two interests:
\(0.2544P=0.24P+720\)
\(0.0144P=720\)
\(P=50000\), so Anuj invested ₹50,000