business math
posted by jama .
Your brother just won the Power Ball lottery. He has the choice of $10,000,000 today or 30year annuity of $500,000, with the first payment coming today. What rate of return is built into the annuity?

Let the builtin interest rate be constant and equal to i.
The future value of the lump sum, S, after 30 years is
S=10000000*(1+i)^30
The future value of the 30 installments, P, at the end of the payments is:
500000*((1+i)^301)/i
Equate S and P and solve by the bisection method or trial and error.
I get about 2.8%.