business math

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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?

  • business math -

    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%.

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