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## anonymous 4 years ago 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]

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1. anonymous

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?

2. anonymous

darn im not this high in math...

3. anonymous

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 4. anonymous i used this because shouldn't i find the Present Value? 5. anonymous $12000\left(\frac{1-(1.089)^{-20}}{0.089}\right)$ 12000 because 1000 every month which means 12000 every year 6. anonymous 110328. 7. anonymous hmm that's still not$111 943.89 though. :S sorry D:

8. anonymous

ok , getting there

9. anonymous

yep. for sure.

10. anonymous

what grade is that, btw?

11. anonymous

grade 11 financial applications (X

12. anonymous

are you sure your answer is absolutely correct, because I tried everything

13. anonymous

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

14. anonymous

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.

15. anonymous

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.

16. anonymous

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

17. anonymous

^20 **

18. anonymous

/(-R)*

19. anonymous

$\left[12000\left(\frac{1-(r)^{-n}}{r}\right)\right.$

20. anonymous

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 !

21. anonymous

np

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