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

To find the amount that Shyam will receive, we use the formula for compound interest, particularly for compounding more frequently than annually. Here, the interest is compounded half-yearly.

Given:

• Principal, \(P = ₹4096\)
• Rate of interest per annum, \(R = 12 \frac{1}{2}\%\) or \(12.5\%\)
• Time period, \(T = 18\) months or \(\frac{3}{2}\) years
• Since the interest is compounded half-yearly, the effective rate \(R_h\) is half of the annual rate, and the time in terms of compounding periods: \(n\):

Calculation:

• Annual rate: \(R = 12.5\%\)
• Half-yearly rate \(R_h = \frac{12.5}{2} = 6.25\%\)
• Time: \(T = \frac{3}{2}\) years = 3 half-years.

The formula for the compound amount when interest is compounded half-yearly is:

\(A = P \left(1 + \frac{R_h}{100}\right)^n\)

Substituting the values, we get:

\(A = 4096 \left(1 + \frac{6.25}{100}\right)^3\)

\(A = 4096 \left(1.0625\right)^3\)

Calculating further:

\(A = 4096 \times (1.0625)^3 = 4096 \times 1.191016\)

\(A = 4880.96164\)

Rounding to the nearest rupee, Shyam will receive approximately ₹4913.

Conclusion:

The correct option is ₹4913.