Find the present value of a perpetuity of rs 18,000 payable at the end of 6 months, if the money is worth 8% p.a. compounded semi-annually.
just plug your numbers into the usual PV formula.
Also, I don't see where you have mentioned the discount rate.
@oobleck
8% p.a. compounded semi-annually is discounted rate
You just want the amount of money which will generate 18,000
at 4% each half year,
that is simply
PV(.04) = 18,000
PV = 450,000
that is, 4% of 450,000 = 18,000, pay it out as a scholarship or whatever,
gets you back to 450,000, another half year ---> 18,000 "perpetually" etc
To find the present value of a perpetuity, we need to use the formula for the present value of a perpetuity:
PV = PMT / r
Where:
PV = Present Value
PMT = Payment per period
r = Interest rate
In this case, the payment per period is Rs 18,000, and the interest rate is 8% p.a. compounded semi-annually.
First, we need to convert the interest rate to a semi-annual rate. Since the interest is compounded semi-annually, the interest rate per period would be half of the annual rate. So, the semi-annual interest rate would be 8% divided by 2, which is 4%.
Now, we can substitute the values into the formula:
PV = 18,000 / 0.04
PV = 450,000
Therefore, the present value of the perpetuity is Rs 450,000.