Your brother just won the Power Ball lottery. He has the choice of $10,000,000 today or 30-year annuity of $500,000, with the first payment coming today. What rate of return is built into the annuity?
Let the built-in 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)^30-1)/i Equate S and P and solve by the bisection method or trial and error. I get about 2.8%.