Question

Find the amount which Shyam will get on ₹4096, if he gave it for 18 months at \(12\frac{1}{2}%\) per annum, interest being compounded half yearly.

• A. ₹5813
• B. ₹4515
• C. ₹4913
• D. ₹5713

Hint:

For half-yearly compounding, divide the annual rate by 2 and multiply the time by 2.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Compound interest compounded half-yearly: rate = half of annual rate, time = \(n \times 2\).

Step 2: Detailed Explanation:
Principal \(P = 4096\)
Rate = \(12\frac{1}{2}% = \frac{25}{2}%\) per annum.
Half-yearly rate = \(\frac{25}{4}% = \frac{25}{400} = \frac{1}{16}\)
Time = 18 months = \(1.5\) years = 3 half-years.
Amount \(A = P(1 + r)^n = 4096(1 + \frac{1}{16})^3\)
\(A = 4096(\frac{17}{16})^3 = 4096 × \frac{4913}{4096} = 4913\)

Step 3: Final Answer:
Shyam will get ₹4913.