Question

At what rate of interest per annum will the present value of a perpetuity of Rs. 500 payable at the end of every 6 months be Rs. 10,000?

• A. 15%
• B. 10%
• C. 20%
• D. 25%

Hint:

Use PV = C / i with i as the rate for one 6 month period, then double it for the annual rate.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A perpetuity is a payment that continues forever. Its present value is the payment divided by the interest rate for one payment period. The payment here is made every 6 months, so the rate must be the rate for 6 months.

Step 2: Key Formula or Approach:
\(PV = \frac{C}{i}\), where \(C\) is the payment each period and \(i\) is the interest rate per period.

Step 3: Detailed Explanation:
Here \(C = 500\) and \(PV = 10000\). The period is 6 months.
\[ i = \frac{500}{10000} = 0.05 = 5\% \text{ per half year} \]
There are two half years in one year, so the annual rate is:
\[ 2 \times 5\% = 10\% \text{ per annum} \]

Step 4: Check the other options.
At 15%, the half yearly rate is 7.5% and the present value is 500/0.075, which is about 6,667. At 20%, it is 500/0.10 = 5,000. At 25%, it is 500/0.125 = 4,000. None of these equals 10,000, so they are wrong.

Final Answer:
The annual rate of interest is 10%. \[ \boxed{10\%} \]