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The present value of a sequence of payments of Rs. 2000 made at the end of every 6 months and continuing forever, if money is worth 8% per annum compounded semi-annually, is:

Solution

✅ Correct Option: 2

This is a perpetuity problem where payments of Rs. 2000 continue forever at the end of every 6 months.

Given information:

Payment = Rs. 2000

Period = 6 months (semi-annually)

Interest rate = 8% per annum compounded semi-annually

Number of payments = Infinite


The interest is 8% per year, but payments occur every 6 months.

Semi-annual interest rate:

i=8%2i = \frac{8\%}{2}

i=4%i = 4\%

i=0.04i = 0.04


For a perpetuity, the present value formula is:

PV=PiPV = \frac{P}{i}

Where PP is the payment per period and ii is the interest rate per period.


Substituting the values:

PV=20000.04PV = \frac{2000}{0.04}

PV=50,000PV = 50,000

Therefore, the present value is Rs. 50,000.

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