Question

Michael has just won some money on a game show! He has the option to take a lump sum payment of $700,000 now or get paid an annuity of $3,600 at the beginning of each month for the next 20 years. Assuming the growth rate of the economy is 3.4% compounding annually over the next 20 years, which is the better deal for Michael and by how much?

Answer 1

Lump Sum:\[$700,000(1.034)^{20}=$1,366,182.81\]

Answer 2

\[\large 700,000*(1+0.034)^{20} =1,366,182.81\]
\[\large 3,600*12*(1+0.034)^{20}+3,600*12*(1+0.034)^{19}\\\large .... 3,600*12*(1+0.034) =1,250,318.76\]

Answer 3

The last one can also be written like this (which obviously gives the same answer):
\[\large 3600*12*\frac{ (1+0.034) ^{20 + 1} - (1 + 0.034) }{ 0.034 }\]