Question:
A sum of money \(P\) is invested at compound interest of 12% per annum, compounded annually. If the compound interest accrued in the third year is ₹2,822.40, find the principal sum \(P\).
एक धनराशि \(P\) को 12% वार्षिक चक्रवृद्धि ब्याज पर निवेश किया जाता है, जो वार्षिक रूप से संयोजित होता है। यदि तीसरे वर्ष में अर्जित चक्रवृद्धि ब्याज ₹2,822.40 है, तो मूलधन \(P\) ज्ञात कीजिए।
Options:
- ₹20,000
- ₹18,500
- ₹22,000
- ₹25,000
- ₹20,000
- ₹18,500
- ₹22,000
- ₹25,000
Correct Answer: a)
Explanation:
Interest for the 3rd year alone is given by:
\(I_3 = A_3 – A_2 = P(1 + r)^3 – P(1 + r)^2 = P(1 + r)^2 \cdot r\).
Here \(r = 0.12\), \(1 + r = 1.12\).
\(I_3 = P \times (1.12)^2 \times 0.12 = 2822.40\).
\((1.12)^2 = 1.2544\).
\(1.2544 \times 0.12 = 0.150528\).
\(P = \frac{2822.40}{0.150528} = 20,000\).
Hence, the principal sum is ₹20,000.
\(I_3 = A_3 – A_2 = P(1 + r)^3 – P(1 + r)^2 = P(1 + r)^2 \cdot r\).
Here \(r = 0.12\), \(1 + r = 1.12\).
\(I_3 = P \times (1.12)^2 \times 0.12 = 2822.40\).
\((1.12)^2 = 1.2544\).
\(1.2544 \times 0.12 = 0.150528\).
\(P = \frac{2822.40}{0.150528} = 20,000\).
Hence, the principal sum is ₹20,000.
केवल तीसरे वर्ष का चक्रवृद्धि ब्याज:
\(I_3 = A_3 – A_2 = P(1 + r)^2 \cdot r\)
यहाँ \(r = 0.12\), \(1 + r = 1.12\)
\(P \times (1.12)^2 \times 0.12 = 2822.40\)
\(P \times 1.2544 \times 0.12 = 2822.40\)
\(P \times 0.150528 = 2822.40\)
\(P = \frac{2822.40}{0.150528} = 20,000\) रुपये।
\(I_3 = A_3 – A_2 = P(1 + r)^2 \cdot r\)
यहाँ \(r = 0.12\), \(1 + r = 1.12\)
\(P \times (1.12)^2 \times 0.12 = 2822.40\)
\(P \times 1.2544 \times 0.12 = 2822.40\)
\(P \times 0.150528 = 2822.40\)
\(P = \frac{2822.40}{0.150528} = 20,000\) रुपये।