I dont know how to solve this question , can someone help me please ? thank you :)


You have just won at National Loto (Congratulations!) and we give you the choice between the following prices:
1. $60 000 at the end of every year during 10 years;
2. $70 000 at the beginning of every year during 8 years;
3. $100 000 at the end of every period of two years, during 12 years;
4. $2 700 at the beginning of every month, and that, until your death (suppose that you are young person and that you are going to live very very old. As a consequence, you can treat this pension as an eternity.).
You consider that you will be able to invest your money at an average rate of 8% (annual real) during all these periods.
a) Which option will you choose?
b) Let us suppose that you choose the 1st option and that you have the possibility of asking for the following modifications on the payment modalities of your price.
Instead of receiving 10 payments of $60 000 at every end of the year, you would rather like to receive 5 equal payments. The first one of these payments would be made, the 2nd in one year, the 3rd in three years, the 4th in six years and, finally, the last one in seven years.

What would be the value of those equal payments?