Answer:
$102,677.20
Step-by-step explanation:
The present value of an annuity due is determined by the following expression:
Where 'P' is the amount of each payment received, 'r' is the interest rate on the investment and 'n' is the number of yearly payments.
With 20 annual payments of $10,000 at a rate of 8.5%, the present value is:
The present value of your winnings is $102,677.20.
I have an expression
floating around in my head; let's see if it makes sense.
The variance of binary valued random variable b that comes up 1 with probability p (so has mean p) is
That's for an individual sample. For the observed average we divide by n, and for the standard deviation we take the square root:
Plugging in the numbers,
One standard deviation of the average is almost 2% so a 27% outcome was 3/1.9 = 1.6 standard deviations from the mean, corresponding to a two sided probability of a bit bigger than 10% of happening by chance.
So this is borderline suspect; most surveys will include a two sigma margin of error, say plus or minus 4 percent here, and the results were within those bounds.