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If the money is worth 8% per annum compounded semi-annually, then the present value of a sequence of payments of ₹1,000 made at the end of every 6 months and continuing forever, is:

Solution

✅ Correct Option: 2

The question asks for the present value of payments of ₹1,000 made at the end of every 6 months continuing forever.

This is a perpetuity problem since payments are equal, occur at regular intervals, and continue indefinitely.


The annual interest rate is 8% compounded semi-annually. Since payments occur every 6 months, the relevant interest rate is the semi-annual rate.

Semi-annual rate =8%2=4%= \dfrac{8\%}{2} = 4\%

Converting to decimal: i=0.04i = 0.04


For a perpetuity, the present value formula is:

PV=AiPV = \dfrac{A}{i}

Where:

A=A = payment amount =₹1,000= ₹1,000

i=i = interest rate per period =0.04= 0.04


Substituting the values:

PV=1,0000.04PV = \dfrac{1,000}{0.04}

PV=25,000PV = 25,000

Therefore, the present value is ₹25,000.

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