I was watching CFA level1 videos and found this odd question.
Elmer has won his $4 million state lottery and has been offered 20 annual payments of $200,000 each beginning today or a single payment of $2,267,000. What is the annual discount rate used to calculate the lump-sum payout amount?
I know how to type in calculator by Begin Mode, N=20, FV=0, PMT=-200,000, PV=2,267,000 ANS: I/Y = 7%
However, I am interested in mathematical calculation. I have tried EMI, i=N√FVPV−1, etc. equations. Doesn't see one of them working. I am wondering which equation is used for calculation interest rate of lump sum? Why following formula doesn't work? -200,000 * (I/Y**20) = 2,267,000