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could someone please help me find my R value for this equation? i'm not quite sure as to what it should be to solve for the equation PV= R [1-(1+i)^-n/i]

Mathematics
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A lottery to raise a funds for a hospital is advertising a $240 000 prize. The winner will receive $1000 ever month for 20 years., starting a year from now. a) if the interest is 8.9% per annum, compounded annually, how much must be invested not to have the money to pay this prize?
darn im not this high in math...
hm.. the way i did it was like this \[240000\left[ 1-(1.089)^{-20} / 0.089 \right]\] but i got the wrong answer. the answer should be $111 943.89 but... i haven't really gotten that yet.. :S

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i used this because shouldn't i find the Present Value?
\[12000\left(\frac{1-(1.089)^{-20}}{0.089}\right)\] 12000 because 1000 every month which means 12000 every year
110328.
hmm that's still not $111 943.89 though. :S sorry D:
ok , getting there
yep. for sure.
what grade is that, btw?
grade 11 financial applications (X
are you sure your answer is absolutely correct, because I tried everything
that's what the answer at the back of the book says. and yeah.. im trying different possibilities as well.. but nothing's been working for me either
really? :S how did you get that? and yea i know for a fact that i can't trust some of the answers in the back of the book.
1 st Year = PV 2nd Year= PV(1+R)-12000 3rd Year= (PV (1 + R)^2 - 12000 (1 + R)) - 12000 21th Year =(PV(1+R)^20)- 12000((1+R)^0+(1+R)^1+....(1+R)^19) rewrite using geometric sum \[\text{PV}(1+R)^{20}-12000\frac{\left(1-(1+R)^{20}\right)}{(-R)}\text{==}0\] we know R, so solve for PV and I get PV = 110328.
hm, that seems to be the closest the answer could get to 111 943. 89 so i guess i'll stick with it for now until i get back to school. i'll ask my teacher if there was a typo in the answer or something.. so the equation is PV(1+R)20−12000(1−(1+R)20)(−R)=0 ? right? R=280000
^20 **
/(-R)*
\[\left[12000\left(\frac{1-(r)^{-n}}{r}\right)\right.\]
alright. i'll just keep it like this for now. and then when i get back to school i'll ask my teacher. thanks for the help imran !
np

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