I have a finance question and would appreciate if I could get some help on how to solve this one!
The Question is the following: Imagine you won a lottery and you are given two choices to receive the prize. You can either receive 50,000 annually for the next 20 years (i.e. for a total of $1,000,000 over 20 years) or a single payment of 400,000 immediately (now). If you expect to make 6% annually on your investment, which payment choices should you choose? Why?
Assume there is no taxes involved and you can get the 6% interest on the $50,000 you receive every year. I have reached the conclusion that accepting the one time sum will be a better option because getting a 6% interest on that over the course of 20 years will produce a greater sum, but I don't know how I could answer it, if I needed to get marks for it.
Hint: Take into account that you have to capitalize each 50,000 payment. You would have something like:
$V_{20} = 50000\cdot 1.06^{20} + 50000\cdot 1.06^{19} + ... + 50000\cdot 1.06^{1} = \sum_{i=1}^{20}50000\cdot 1.06^i$ (geometric series)
On the other hand for the 400,000 you have:
$S_{20} = 400000 \cdot 1.06^{20}$
(*You could also discount and compare the present value $V_0$ and $S_0$)