Question:
If Rs. 40,000 is invested at a compound interest of 16% p.a. for 18 months, compounded every 6 months, find the interest earned.
यदि ₹40,000 की राशि 16% वार्षिक चक्रवृद्धि ब्याज की दर से 18 महीने के लिए निवेश की जाती है, और ब्याज अर्धवार्षिक रूप से संयोजित होता है, तो अर्जित ब्याज ज्ञात कीजिए।
Options:
- Rs. 9,856.76
- Rs. 10,388.48
- Rs. 11,200.98
- Rs. 8,960.56
- ₹9,856.76
- ₹10,388.48
- ₹11,200.98
- ₹8,960.56
Correct Answer: b)
Explanation:
Principal \(P = \text{Rs. } 40,000\). Rate per compounding period (half-yearly) \(r = 16\% / 2 = 8\%\). Time = 18 months = 3 half-years (\(n = 3\)).
Amount \(A = P\left(1 + \dfrac{r}{100}\right)^n = 40000(1.08)^3 = 40000 \times 1.259712 = \text{Rs. } 50,388.48\).
Compound Interest \(CI = A – P = 50388.48 – 40000 = \text{Rs. } 10,388.48\).
मूलधन \(P = ₹40,000\)। अर्धवार्षिक ब्याज दर \(r = 16\% / 2 = 8\%\)। समय = 18 महीने = 3 अर्धवर्ष (\(n = 3\))।
मिश्रधन \(A = P\left(1 + \dfrac{r}{100}\right)^n = 40000(1.08)^3 = 40000 \times 1.259712 = ₹50,388.48\)।
चक्रवृद्धि ब्याज \(CI = A – P = 50388.48 – 40000 = ₹10,388.48\)।