A judge denied a 94yearold woman s attempt to force a Lotter

\"A judge denied a 94-year-old woman s attempt to force a Lottery Commission to pay her $3.64 million winnings up front on the grounds that she otherwise won\'t live long enough to collect it all. The woman already received an immediate payment of $156,821, and she will receive 12 annual gross checks of $290,265. If a buyer offers to pay the woman $2.1 million for the 12 annual gross checks of $290,265, what is the buyer\'s annual interest rate? Enter your answer as a percentage between 0 and 100.\"

Solution

assume annual interest rate=r

then we will use present value equation

290265/(1+r)^1+290265/(1+r)^2+290265/(1+r)^3+290265/(1+r)^4+290265/(1+r)^5+290265/(1+r)^6+290265/(1+r)^7+290265/(1+r)^8+290265/(1+r)^9+290265/(1+r)^10+290265/(1+r)^11+290265/(1+r)^12=(2.1*1000000)

now you need to use hit and trial method to find the value of r where right side and left side of the equation are equal

you need to continue trying until you reach required rate

here after trying many times , I get value of r=8.80%

so the anwer is buyer\'s interest rate =8.80%

the above is answer