You're working on a project that will take you 30 days to finish, choose your payment method. You are paid a total of $2,000,000 on the first day? OR You are paid everyday of the project, each day you're paid double of what you were paid on the previous day. On the first day, you're paid $0.01 Which is the best choice?
+118608 1,2,4,8,....2^(n-1).......2^29
a=1, r=2 n=30
$$\\S_n=\frac{a(r^n-1)}{r-1}\\\\
S_{30}=\frac{1(2^{30}-1)}{2-1}\\\\
S_{30}=2^{30}-1\\\\$$
$${{\mathtt{2}}}^{{\mathtt{30}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{1\,073\,741\,823}}$$ cents
So the daily payment will add up to $10,737,418.23
The up front amount is $2,000,000.00
Well the daily amount is more than 5 times the up front payment.
+118608 1,2,4,8,....2^(n-1).......2^29
a=1, r=2 n=30
$$\\S_n=\frac{a(r^n-1)}{r-1}\\\\
S_{30}=\frac{1(2^{30}-1)}{2-1}\\\\
S_{30}=2^{30}-1\\\\$$
$${{\mathtt{2}}}^{{\mathtt{30}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{1\,073\,741\,823}}$$ cents
So the daily payment will add up to $10,737,418.23
The up front amount is $2,000,000.00
Well the daily amount is more than 5 times the up front payment.
