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Answer :
The first Option will be the present value of the lottery which is to be compared with the present values of the other two options at 7%, 8% and 9%.
Here we can write
If she thinks she can earn 7% annually, which should she choose?.
Since
So she should Choose second option, as the time horizon is small and she can reinvest the proceed in the same to get much higher return in the same span as given in option three. From option three she will get 69.49-62 = 7.49 while reinvesting in the second option will fetch her 3 x 4.72-7.49=14.16-7.49=6.67 Million Extra in the span of thirty year.
If she expects to earn 8% annually, which is the best choice?
She will choose the second one and reinvest the proceeds in the same to get extra return much better than the third and first option.
If she expects to earn 9% annually, which option would you recommend?
In this case she will choose the first one as the PV of other two are less than the first.
She will choose the first one as there is minimum gain of only 1.04 million considering the time horizon she will better invest somewhere else which will give her better return.
How interest rates influence her choice.
Money in the hand is better than money in the future considering the time value of money at higher interest rates the present values will tend to be low due to discounting factor hence lower interest rates are preferred and lower time horizon taking into consideration the liquidity factor or the locking period for funds.
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