## chrissytt17 3 years ago a person wishes to invest M dollars at t eh end of each month from January 2000 until the end of December 2003. If the account gives interest at the annual rate of 18% compounded monthly and the individual wishes to have $100,000 by the end of 2003, how much should be invested each month? • This Question is Closed 1. chrissytt17 No i don't 2. sheg it is $A=P\times{(1+r)^{n}}$ where A = Amount P = Principal r = Rate of interest n = number of time period 3. sheg ok now tell me for how many moths you will be investing?? 4. chrissytt17 so for 3 years that's 36 months 5. sheg you started investing from Jan 200 - Dec 2003 right it is 36 months 6. chrissytt17 A=100,000x(1+18%)^36 7. chrissytt17 a=100,000 (19)^36 8. sheg so here n = 3yrs = 36 months r = 18% per annum but this will get compounded monthly so it cannot be 18% 9. chrissytt17 can i leave it in the annual form and just do A=100,000x(19)^3 ? 10. sheg so your formula will change right the formula that i had given u is the general formula now when it is compounded monthly in that case the formula would be $A = P\times{(1+{{r}\over{12}})^{12n}}$ 11. sheg @chrissytt17 here principal is unknown 12. sheg are you getting my point? 13. chrissytt17 i thought the principal is the amount that the individual wants 14. sheg no what you want that you will get at what time???? 15. sheg the individual wishes to have$100,000 by the end of 2003, how much should be invested each month?

16. chrissytt17

100,000=Px(1+r/12)^12n

17. sheg

where r = 18% but when you are plugging in the value of r that time convert it into decimal so r = 0.18

18. chrissytt17

100,000= P x (1+.18/12)^12*3 ?

19. chrissytt17

100,000= P x (1.015)^36

20. chrissytt17

am i on the right track?

21. sheg

wait let me cross check it

22. chrissytt17

i came up with about 58,513.75

23. sheg

no it is not correct

24. chrissytt17

I followed the formula

25. chrissytt17

I think I am lost

26. sheg

hey i was not telling you about the Annuity do you know about it?

27. chrissytt17

no

28. sheg

you are in which class

29. chrissytt17

math 118

30. sheg

ok do you know about time value of money

31. chrissytt17

I'm not sure

32. sheg

$100000 = P \times \sum_{n=1}^{36}(1.015)^n$\]

33. sheg

ok solve this one you will get the exact value

34. sheg

the second factor on RHS is called as Present Value Interest Factor of Annuity

35. chrissytt17

I don't know what that symbol is

36. sheg

it is summation