5-40. (Future and present v alue using a calculator) Bill Gates\'s Billions! O v

Question

5-40. (Future and present value using a calculator) Bill Gates's Billions! Over the past few years
Microsoft founder Bill Gates's net worth has fluctuated between $30 and $130 billion. In late 2004
it was about $30 billion (in late 2004 he owned just over 1.1 billion shares of Microsoft, and
Microsoft's stock was trading at $27.29) after he reduced his stake in Microsoft from 21 percent to
around 14 percent by moving billions into his charitable foundation. Let's see what Bill Gates 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, 379 years later in 2005, Bill Gates wants to buy the island from the "current
natives." How much would Bill have to pay for Manhattan if the "current natives" want a 6 percent annual return on the original $24 purchase  price?  Could he afford it?  
b. (This part requires nonannual compounding using a calculator) How much would Bill have to pay for Manhattan if the "current natives" want a 6% return compounded monthly on the original $24 purchase price?

Explanation / Answer

For both a and b, I'll use the equation V= P( 1 + r/n)^nt. For a), r=0.06, n=1, t=379 and P=24. So V=24(1.06)^379=93.57 BILLION. Since this is well over 30 billion, Bill cannot afford this. The only change on b) is that n=12. So now V=24(1.005)^(12*379), about 170.4 billion.

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