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

16. chrissytt17 Group Title

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

17. sheg Group Title

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 Group Title

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

19. chrissytt17 Group Title

100,000= P x (1.015)^36

20. chrissytt17 Group Title

am i on the right track?

21. sheg Group Title

wait let me cross check it

22. chrissytt17 Group Title

i came up with about 58,513.75

23. sheg Group Title

no it is not correct

24. chrissytt17 Group Title

I followed the formula

25. chrissytt17 Group Title

I think I am lost

26. sheg Group Title

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

27. chrissytt17 Group Title

no

28. sheg Group Title

you are in which class

29. chrissytt17 Group Title

math 118

30. sheg Group Title

ok do you know about time value of money

31. chrissytt17 Group Title

I'm not sure

32. sheg Group Title

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

33. sheg Group Title

ok solve this one you will get the exact value

34. sheg Group Title

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

35. chrissytt17 Group Title

I don't know what that symbol is

36. sheg Group Title

it is summation