Posted by **jama** on Sunday, July 3, 2011 at 11:55pm.

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 -
**MathMate**, Monday, July 4, 2011 at 4:44pm
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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