Jeff Bezos has a private wealth of about $$127$ billion $($data: Bloomberg, $31/10/2022).$ Let$$s see what Jeff Bezos can do with his money in the following problems.

a$.$ I$$ll take Manhattan? Manhattan$$s native tribe sold Manhattan Island to Peter Minuit for $$24$ in $1626.$ Now, $396$ years later in $2022,$ Jeff Bezos wants to buy the island from the $$current natives.$$ How much would Bezos have to pay for Manhattan if the $$current natives$$ want a $5\%$ annual return on the original $$24$ purchase price? Could he afford it$?(5$ points$)$

b$.$ How much would Jeff have to pay for Manhattan if the $$current natives$$ want a $5\%$ return compounded monthly on the original $$24$ purchase price? $(5$ points$)$

c$.$ Austria? Jeff Bezos enjoys skiing so he plans to purchase the whole country of Austria at the price of the current value of GDP of $$404$ billion $($data: World Bank, $2021).$ How much would Mr$.$ Bezos have to invest today at $10$ percent compounded annually in order to purchase Austria in $10$ years at this price? $(5$ points$)$

d$.$ If Bezos decides to set up a foundation with funding of $$1$ billion that he will contribute to the saving account at the end of each year during the next $20$ years and the bank offers him a return of $6\%,$ how much will be generated on this saving account