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Homework answers / question archive / You have just won a two-part lottery! The first part will pay you $50,000 at the end of each of the next 20 years
You have just won a two-part lottery! The first part will pay you $50,000 at the end of each of the next 20 years. The second part will pay you $1,000 at the end of each month over the same 20 year period. Assuming a discount rate of 12%, what is the present value of your winnings? O $464,292 O $495,048 O $567,572 $529,303 O $610,462
Ans) $ 464,292
PV of first part
Here Annuity = 50000 $
r = rate of interest = 12%
n = no of payments = 20
Thus present value of annuity = annuity[1-(1/(1+r)^n / r]
= 50000[1-(1/(1+12%)^20 / 12%]
= 50000[1-(1/1.12)^20 /12%]
= 50000[1-0.1037 / 0.12]
= 50000[0.8963/0.12]
= 50000 x 7.4694
= 373472.18 $
PV of second part
Here Annuity =1000$
r = rate of interest = 12%/12 = 1%
n = no of payments = 20 x 12 = 360
Thus present value of annuity = annuity[1-(1/(1+r)^n / r]
= 1000[1-(1/(1+1%)^240 / 1%]
= 1000[1-(1/1.01)^240 /1%]
= 1000[1-0.09181 / 0.01]
= 1000[0.90819/0.01]
= 1000 x 90.8191
= 90819.42 $
Thus PV of total winnings = 373472.18 + 90819.42
=464291.60 $
i.e 464292 $
