Question:
Find the compound interest on Rs. 16,000 at 10% per annum for \(1\frac{1}{2}\) years, compounded half-yearly.
16,000 रुपये पर 10% वार्षिक दर से \(1\frac{1}{2}\) वर्ष का अर्धवार्षिक संयोजित चक्रवृद्धि ब्याज ज्ञात कीजिए।
Options:
- Rs. 2,522
- Rs. 2,400
- Rs. 2,640
- Rs. 2,480
- 2,522 रुपये
- 2,400 रुपये
- 2,640 रुपये
- 2,480 रुपये
Correct Answer: a)
Explanation:
Principal \(P = 16,000\).
Half-yearly rate \(r = 10 / 2 = 5\%\).
Number of half-year periods \(n = 1.5 \times 2 = 3\).
Amount \(A = P(1 + r/100)^3 = 16,000 \times (1.05)^3 = 16,000 \times 1.157625 = 18,522\).
\(\text{CI} = 18,522 – 16,000 = \textbf{Rs. 2,522}\) (Option a).
अर्धवार्षिक दर \(r = 5\%\), अवधि \(n = 3\).
मिश्रधन \(A = 16,000 \times (1.05)^3 = 18,522\) रुपये।
चक्रवृद्धि ब्याज = \(18,522 – 16,000 = \textbf{2,522 रुपये}\) (विकल्प a)।