Expert: Scott A Wilson - 1/23/2010

Question
Patrick wins $250,000 in the lottery. He wants to know best way to invest. He decides that if he invest $250,000 for 30 years at 10% he would have $4,362,351 using p(1+i)n. $250,000(1+.10)30 His friend Josh says "hey you would never get 10% each and every year for 30 years" Josh says we will figure that you get 17.5% 70% of the time and a loss of -7.5% 30% of the time. That would produce an average return of 0.7(17.5%)+0.3(-7.5%)=10%. He thinks that the amount would be the same because of the 10%. Is Josh correct?

Answer
At 10%, 1+i is 1.1.  To the 30th is 17.45.

The other one is at 17.5% interest 70% of the time and at -7.5% interests 30% of time time.
Since 70% of 30 years is 21 and 30% of 30 years is 9, that would be
(1.175^21)(0.925^7) = 17.13.

From this, it can be seen that the first option is better on the average.
No, Josh is not correct.


Now if the difference between 17.45 and 17.13 is looked at, that is only 0.32.
That is less than a 2% difference between them.