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:
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
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:
For a perpetuity, the present value formula is:
Where is the payment per period and is the interest rate per period.
Substituting the values:
Therefore, the present value is Rs. 50,000.
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2026: 22 May Shift 2