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nslesin

  • 2 years ago

Can someone assist me with this problem please.

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  1. nslesin
    • 2 years ago
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  2. ganeshie8
    • 2 years ago
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    use the compound interest formula \(\large A = P(1+\frac{r}{n})^{nt}\) \(P\) = 200 \(r\) = 3% = 0.03 \(n\) = 12 (months) \(t\) = 10 (years)

  3. ganeshie8
    • 2 years ago
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    plugin the values and see wat u get

  4. nslesin
    • 2 years ago
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    \[A= 200 (1+ \frac{ 0.03 }{ 12 }) ^{(12\times ^{10)}}\]

  5. ganeshie8
    • 2 years ago
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    yes ! give it to ur calculator

  6. nslesin
    • 2 years ago
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    So I do \[(1+0.03\div12)\]first?

  7. ganeshie8
    • 2 years ago
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    yes

  8. nslesin
    • 2 years ago
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    \[A= 200 (1 + 0.0025) ^{12\times10}\]

  9. ganeshie8
    • 2 years ago
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    yes

  10. nslesin
    • 2 years ago
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    \[A= 200(1.0025)^{(120)}\] I am unsure which part to do first.

  11. ganeshie8
    • 2 years ago
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    exponent first

  12. ganeshie8
    • 2 years ago
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    \((1.0025)^{120}\)

  13. nslesin
    • 2 years ago
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    269.87.. that seems like a small #

  14. phi
    • 2 years ago
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    You should be using the formula that gives you the future value of a stream of regular payments. see http://www.annuityformulas.org/future-value-of-regular-payments.html

  15. ganeshie8
    • 2 years ago
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    thats all you wud get at 3% interest rate for 10 years this is not an annuity setup @phi

  16. phi
    • 2 years ago
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    For Zach, the equation is \[ FV= pymt \cdot \frac{ (1+i)^n - 1}{i} \] where n is 10 years, pymt is 2400 and i is 0.03

  17. nslesin
    • 2 years ago
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    Yolanda 296.87?

  18. phi
    • 2 years ago
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    no, Yolanda is depositing 200 per month, or 200*12= 2400 per year for 10 years = 24,000 that is if there was no interest. But there is 3% interest, so it will be bigger than that

  19. ganeshie8
    • 2 years ago
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    yes @phi thanks for catching that, weird 260 is small i dint even notice... i need to go run an errand, cya

  20. nslesin
    • 2 years ago
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    @phi so what is the equation set up now im officially confused could u write it step by step for me?

  21. phi
    • 2 years ago
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    I wrote out Zach's can you do that one first ?

  22. nslesin
    • 2 years ago
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    I got 82,400

  23. phi
    • 2 years ago
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    can you show your steps?

  24. nslesin
    • 2 years ago
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    Fv= 2400 x (1+0.03)/0.03

  25. phi
    • 2 years ago
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    that is not the formula. Look more carefully

  26. nslesin
    • 2 years ago
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    fv=2400 x (1+0.03)^(10)-1/0.03?

  27. phi
    • 2 years ago
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    yes but use parens fv=2400 x ( (1+0.03)^(10)-1 ) /0.03?

  28. nslesin
    • 2 years ago
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    27200?

  29. phi
    • 2 years ago
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    ball park, but not exactly what do you get for 1.03^10 ?

  30. phi
    • 2 years ago
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    then subtract 1

  31. nslesin
    • 2 years ago
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    1.343916379

  32. phi
    • 2 years ago
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    yes, now subtract 1 to get .343916379

  33. nslesin
    • 2 years ago
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    then 0.343916379

  34. phi
    • 2 years ago
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    now divide by 0.03

  35. nslesin
    • 2 years ago
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    27,513.31

  36. phi
    • 2 years ago
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    yes, that looks good.

  37. nslesin
    • 2 years ago
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    So thats Zachs. now i have to find balance in Yolanda savings plan after 10 years

  38. phi
    • 2 years ago
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    For Yolanda you use the same formula (they don't say if she deposits the $200 at the end of each month.. but let's assume she does) however, n is in months (so 10*12= 120) and the interest is per month so 0.03/12

  39. nslesin
    • 2 years ago
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    Wait so n= number of years?

  40. phi
    • 2 years ago
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    n is the number of payments

  41. nslesin
    • 2 years ago
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    FV= pymt \[\times (1+i)^n-1\]\[\div i\]

  42. phi
    • 2 years ago
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    yes

  43. nslesin
    • 2 years ago
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    it doesnt say the number of payments

  44. phi
    • 2 years ago
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    it says every month for 10 years how many months in a year ?

  45. nslesin
    • 2 years ago
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    n=120

  46. phi
    • 2 years ago
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    yes

  47. nslesin
    • 2 years ago
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    how do i figure out pymt is i= 0.03?

  48. phi
    • 2 years ago
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    you want i per month. they give you the i for the whole year

  49. nslesin
    • 2 years ago
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    0.03/12?

  50. phi
    • 2 years ago
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    yes

  51. nslesin
    • 2 years ago
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    Argh i hate this 2.5 x 10 ^ -03 how do i do that?

  52. phi
    • 2 years ago
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    you want (1+i)^120 where i= 0.03/12 so do it in steps: 0.03/12 add 1 raise to the 120 power

  53. nslesin
    • 2 years ago
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    yeah im totally confused

  54. phi
    • 2 years ago
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    you are doing \[ FV= pymt \cdot \frac{ (1+i)^n - 1}{i} \] does your calculator have memory, so you can put 0.03/12 into memory ?

  55. nslesin
    • 2 years ago
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    dont think so

  56. phi
    • 2 years ago
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    type parens ( then 1 + 0.03/12 then close ) then ^ then 120

  57. nslesin
    • 2 years ago
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    0.03 ÷ 12?

  58. phi
    • 2 years ago
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    yes

  59. nslesin
    • 2 years ago
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    2.5 x 10 ^ -03 how do i do that?

  60. phi
    • 2 years ago
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    add 1

  61. nslesin
    • 2 years ago
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    i= 5

  62. phi
    • 2 years ago
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    just type into your calculator 0.03 ÷ 12 + 1 enter

  63. phi
    • 2 years ago
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    you will get a number now type ^ 120

  64. nslesin
    • 2 years ago
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    1.349353547

  65. phi
    • 2 years ago
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    then type - 1 (to subtract 1)

  66. nslesin
    • 2 years ago
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    wait 1.0025+1= 2.0025

  67. phi
    • 2 years ago
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    you are doing 1.0025^120 - 1

  68. phi
    • 2 years ago
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    1.0025^120 - 1 you get 1.349353547 -1 and .349353547 now divide by (0.03/12) (or 0.0025)

  69. nslesin
    • 2 years ago
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    but what about the 0.349353547+1?

  70. phi
    • 2 years ago
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    you are doing 1.0025^120 - 1 which gives you 0.349353547 at this point, you do not add +1. the formula says divide by i i is 0.0025 (the same as 0.03/12)

  71. nslesin
    • 2 years ago
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    it just FV= pymt (1.0025)^120 -1

  72. phi
    • 2 years ago
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    you need parens and you need to divide by i \[ FV= pymt \cdot \frac{ (1+i)^n - 1}{i} \]

  73. nslesin
    • 2 years ago
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    whats the pymt?

  74. phi
    • 2 years ago
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    the payment is how much Yolanda is saving each month (how much she is paying into her bank account)

  75. nslesin
    • 2 years ago
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    200

  76. phi
    • 2 years ago
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    yes

  77. nslesin
    • 2 years ago
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    268.87

  78. nslesin
    • 2 years ago
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    that doesnt seem right

  79. phi
    • 2 years ago
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    because it is not correct. you must use the correct formula

  80. nslesin
    • 2 years ago
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    The FV?

  81. phi
    • 2 years ago
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    yes \[ FV= pymt \cdot \frac{ (1+i)^n - 1}{i}\]

  82. nslesin
    • 2 years ago
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    200 (1+0.03/12)^120-1

  83. phi
    • 2 years ago
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    you forgot the divide by i

  84. nslesin
    • 2 years ago
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    1+0.03/12?

  85. phi
    • 2 years ago
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    I am saying that this is not correct 200 (1+0.03/12)^120-1 the correct formula is 200 ( (1+0.03/12)^120-1)/ (0.03/12)

  86. nslesin
    • 2 years ago
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    oh i forgot to add divide by i

  87. nslesin
    • 2 years ago
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    748.86

  88. phi
    • 2 years ago
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    you are not doing the calculation correctly type this into the google search window 200 * ( (1+0.03/12)^120-1)/ (0.03/12)=

  89. nslesin
    • 2 years ago
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    27948.28

  90. phi
    • 2 years ago
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    yes

  91. nslesin
    • 2 years ago
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    and zach was what we did before which was 27,513.31

  92. nslesin
    • 2 years ago
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