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anonymous

  • one year ago

You decide to put $100 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?

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  1. anonymous
    • one year ago
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    @ospreytriple

  2. anonymous
    • one year ago
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    @Mertsj

  3. anonymous
    • one year ago
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    Do you know the compound interest formula from your course?

  4. anonymous
    • one year ago
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    yeah

  5. anonymous
    • one year ago
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    a(t)=p(1+r)^t

  6. anonymous
    • one year ago
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    OK. It looks like we want a(t) to be $3000 cause that's how much needs to be saved. p is the present value. How much is that?

  7. anonymous
    • one year ago
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    100

  8. anonymous
    • one year ago
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    OH!! In your previous question, the right hand side of the equation was NEGATIVE, so the correct answer is the negative number. Sorry about that.

  9. anonymous
    • one year ago
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    $100 is correct.

  10. anonymous
    • one year ago
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    The interest rate (r) is a little bit tricky. The question says the nominal yearly interest rate is 2% but it is compounded monthly. Do you know how to get the interest rate in this case?

  11. anonymous
    • one year ago
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    ummm 12??

  12. anonymous
    • one year ago
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    Well, it's 2% per year, but for a month it's going to be 1/12 as much. What do you think?

  13. anonymous
    • one year ago
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    I agree

  14. anonymous
    • one year ago
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    OK. so r = 2% /12. Have to convert that to a decimal. What do you get?

  15. anonymous
    • one year ago
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    0.02

  16. anonymous
    • one year ago
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    Right. But you still have to divide by 12 to get r.

  17. anonymous
    • one year ago
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    ok so 0.02/12 ??

  18. Mertsj
    • one year ago
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    \[A=P(1+\frac{r}{n})^{nt}\] \[3000=100(1+\frac{.02}{12})^{12t}\]

  19. Mertsj
    • one year ago
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    Solve for t

  20. anonymous
    • one year ago
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    That's it. What's r then?

  21. anonymous
    • one year ago
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    3000=100.16667)^12t

  22. anonymous
    • one year ago
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    r is not 0.16667. Try it again

  23. anonymous
    • one year ago
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    r=0.02

  24. anonymous
    • one year ago
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    Remember, we already established that r = 0.02/12. What do you get?

  25. anonymous
    • one year ago
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    0.001666667

  26. anonymous
    • one year ago
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    Great. Now out that value of r into the compound interest formula and what do you get?

  27. Mertsj
    • one year ago
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    r=.02

  28. anonymous
    • one year ago
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    Perhaps you'd like to take over @Mertsj

  29. anonymous
    • one year ago
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    3000=(100.16667)^12t

  30. anonymous
    • one year ago
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    What's 100 + 0.0016667 ?

  31. Mertsj
    • one year ago
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    Continuing: \[\frac{3000}{100}=\frac{100(1+\frac{.02}{12})^{12t}}{100}\]

  32. anonymous
    • one year ago
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    100.0016667

  33. anonymous
    • one year ago
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    30=(1+0.02/12)^12t

  34. anonymous
    • one year ago
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    Great. So you have\[3000 = 100.0016667^{12t}\]Now take the log of both sides

  35. Mertsj
    • one year ago
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    \[300=(1.01666666)^{12t}\]

  36. anonymous
    • one year ago
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    ok so 1og 300=....?

  37. Mertsj
    • one year ago
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    \[\log_{10}300=12t \log_{10}1.0166666666 \]

  38. anonymous
    • one year ago
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    I'm sorry @BellaBlue77 . Our work is being hijacked. I'm out. Good luck.

  39. Mertsj
    • one year ago
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    \[\frac{\log_{10}300}{\log_{10}1.016666666}=12t \]

  40. anonymous
    • one year ago
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    ok hold onn

  41. anonymous
    • one year ago
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    300/ 1.01666666=12t

  42. Mertsj
    • one year ago
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    \[345.07=12t\]

  43. anonymous
    • one year ago
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    28. 76

  44. Mertsj
    • one year ago
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    \[28.8=t\]

  45. anonymous
    • one year ago
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    170.202 years 14.3129 years 171.755 years 168.354 years

  46. anonymous
    • one year ago
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    That's not an answer choice

  47. anonymous
    • one year ago
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    @heretohelpalways @ganeshie8

  48. Mertsj
    • one year ago
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    Error: 3000/100=30

  49. anonymous
    • one year ago
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    yes

  50. Mertsj
    • one year ago
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    \[\frac{\log_{10}30}{\log_{10}1.0166666666}=12t \]

  51. anonymous
    • one year ago
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    ok so 30/1.016666

  52. anonymous
    • one year ago
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    29.5081967232=12t

  53. Mertsj
    • one year ago
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    you have to take the log of those numbers.

  54. anonymous
    • one year ago
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    so log 29.508...?

  55. Mertsj
    • one year ago
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    Do you see that it says log 30?

  56. anonymous
    • one year ago
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    1.46994267012

  57. anonymous
    • one year ago
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    1.47712125472 i mean

  58. anonymous
    • one year ago
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    would 168.354 years be the answer?

  59. Mertsj
    • one year ago
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    I keep getting 17.14

  60. anonymous
    • one year ago
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    I know :( But thats not an answer choice. 170.202 years 14.3129 years 171.755 years 168.354 years see?

  61. anonymous
    • one year ago
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    Oh well, let's call it a day loll

  62. anonymous
    • one year ago
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    If you find the answer, message me pleae, I'll be back tommorw

  63. Mertsj
    • one year ago
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    Starting over: \[3000=100(1+\frac{.02}{12})^{12t}\] \[30=(1+.00166666666)^{12t}\]

  64. Mertsj
    • one year ago
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    \[\frac{\log_{10}30}{\log_{10}1.00166666666666}=12t \]

  65. Mertsj
    • one year ago
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    \[2042.4185=12t\]

  66. Mertsj
    • one year ago
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    \[170.20=t\]

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