A sum of Rs. 1,00,000 invested at r% compounded half yearly will prov…

The correct answer is Option (2) → 1

Payments that go on for ever are a perpetuity. Its present value is the payment divided by the rate per payment period:

    \(\displaystyle P = \frac{R}{i}\)

Here P = 100000 and R = 500 every half-year, so

    \(\displaystyle i = \frac{500}{100000} = 0.005\)

That is 0.5% per half-year. The nominal annual rate compounded half-yearly is twice this:

    \(r = 2\times 0.5 = 1\)

So r = 1 (1% per annum).

Tip: 0.5 (Option (1)) is the rate per half-year; r is the yearly rate, so it must be doubled.