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chrissytt17

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?

  • one year ago
  • one year ago

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  1. chrissytt17
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    No i don't

    • one year ago
  2. sheg
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    it is \[A=P\times{(1+r)^{n}}\] where A = Amount P = Principal r = Rate of interest n = number of time period

    • one year ago
  3. sheg
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    ok now tell me for how many moths you will be investing??

    • one year ago
  4. chrissytt17
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    so for 3 years that's 36 months

    • one year ago
  5. sheg
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    you started investing from Jan 200 - Dec 2003 right it is 36 months

    • one year ago
  6. chrissytt17
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    A=100,000x(1+18%)^36

    • one year ago
  7. chrissytt17
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    a=100,000 (19)^36

    • one year ago
  8. sheg
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    so here n = 3yrs = 36 months r = 18% per annum but this will get compounded monthly so it cannot be 18%

    • one year ago
  9. chrissytt17
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    can i leave it in the annual form and just do A=100,000x(19)^3 ?

    • one year ago
  10. sheg
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    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 \[A = P\times{(1+{{r}\over{12}})^{12n}}\]

    • one year ago
  11. sheg
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    @chrissytt17 here principal is unknown

    • one year ago
  12. sheg
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    are you getting my point?

    • one year ago
  13. chrissytt17
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    i thought the principal is the amount that the individual wants

    • one year ago
  14. sheg
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    no what you want that you will get at what time????

    • one year ago
  15. sheg
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    the individual wishes to have $100,000 by the end of 2003, how much should be invested each month?

    • one year ago
  16. chrissytt17
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    100,000=Px(1+r/12)^12n

    • one year ago
  17. sheg
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    where r = 18% but when you are plugging in the value of r that time convert it into decimal so r = 0.18

    • one year ago
  18. chrissytt17
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    100,000= P x (1+.18/12)^12*3 ?

    • one year ago
  19. chrissytt17
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    100,000= P x (1.015)^36

    • one year ago
  20. chrissytt17
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    am i on the right track?

    • one year ago
  21. sheg
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    wait let me cross check it

    • one year ago
  22. chrissytt17
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    i came up with about 58,513.75

    • one year ago
  23. sheg
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    no it is not correct

    • one year ago
  24. chrissytt17
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    I followed the formula

    • one year ago
  25. chrissytt17
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    I think I am lost

    • one year ago
  26. sheg
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    hey i was not telling you about the Annuity do you know about it?

    • one year ago
  27. chrissytt17
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    no

    • one year ago
  28. sheg
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    you are in which class

    • one year ago
  29. chrissytt17
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    math 118

    • one year ago
  30. sheg
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    ok do you know about time value of money

    • one year ago
  31. chrissytt17
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    I'm not sure

    • one year ago
  32. sheg
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    \[100000 = P \times \sum_{n=1}^{36}(1.015)^n\]\]

    • one year ago
  33. sheg
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    ok solve this one you will get the exact value

    • one year ago
  34. sheg
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    the second factor on RHS is called as Present Value Interest Factor of Annuity

    • one year ago
  35. chrissytt17
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    I don't know what that symbol is

    • one year ago
  36. sheg
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    it is summation

    • one year ago
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