## alexeis_nicole 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]

1. alexeis_nicole

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...

3. alexeis_nicole

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. alexeis_nicole i used this because shouldn't i find the Present Value? 5. imranmeah91 $12000\left(\frac{1-(1.089)^{-20}}{0.089}\right)$ 12000 because 1000 every month which means 12000 every year 6. imranmeah91 110328. 7. alexeis_nicole hmm that's still not$111 943.89 though. :S sorry D:

8. imranmeah91

ok , getting there

9. alexeis_nicole

yep. for sure.

10. imranmeah91

11. alexeis_nicole

12. imranmeah91

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

13. alexeis_nicole

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. alexeis_nicole

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. imranmeah91

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. alexeis_nicole

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. alexeis_nicole

^20 **

18. alexeis_nicole

/(-R)*

19. imranmeah91

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

20. alexeis_nicole

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. imranmeah91

np