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:
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
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
Converting to decimal:
For a perpetuity, the present value formula is:
Where:
payment amount
interest rate per period
Substituting the values:
Therefore, the present value is ₹25,000.
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