present value

QUESTION

I have an answer,I just need to make sure its correct.The Clearinghouse Sweepstakes has just informed you that you have won $1 million. The amount is to be paid out at the rate of $20,000 a year for the next 50 years. With a discount rate of 10%, what is the present value of your prize?My answer: $
We need to find the PV of Annuity of $20,000 for N=50 yrs with Dic rate i=10%. ie PVAn=PMT*PVIFAn,1 = 20000*PVIFA50,10% Looking at Annuity table, we get PVIFA50,10% = 9.9148 So PVA50 = 20,000*9.9148 = $198,296 So PV of prize is $198,296 We can also find the

PV using maths (wout uing the annuity table) PVAn = PMT*[1/i 1/(i*(1 i)^N)] = 20000*[1/0.1 1/(0.1*(1 0.1)^50] ie PVA50 = 20,000*[10 0.0852] = 20,000*9.9148 = $198,296

ANSWER:

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