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anonymous

  • 4 years ago

How long will it take for $2000 to double if it is invested at 6.25% interest compounded continuously? can some show me how to set this problem into this equation A=Pe^rt, please!

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  1. Mertsj
    • 4 years ago
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    \[4000=2000e ^{.0625t}\]

  2. Mertsj
    • 4 years ago
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    \[2=e ^{.0625t}\]

  3. Mertsj
    • 4 years ago
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    \[\ln 2=.0625t(\ln e)\]

  4. Mertsj
    • 4 years ago
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    \[\frac{\ln2}{.0625}=t\]

  5. Mertsj
    • 4 years ago
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    \[11.09 yrs = t\]

  6. anonymous
    • 4 years ago
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    can you please give me a crash course on what you did, Please...

  7. Mertsj
    • 4 years ago
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    Did you understand how the values were substituted into the equation?

  8. anonymous
    • 4 years ago
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    no i didnt

  9. Mertsj
    • 4 years ago
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    A is the amount which was determined to be $4000 because the problem asked how long it would take a $2000 investment to double.

  10. Mertsj
    • 4 years ago
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    If $2000 doubles, it will then be $4000 would you agree?

  11. Mertsj
    • 4 years ago
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    So the problem is really asking "how long will it take $2000 to turn into $4000"

  12. anonymous
    • 4 years ago
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    what does the e stand for?

  13. Mertsj
    • 4 years ago
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    The e is a frequently used mathematical constant. It doesn't stand for anything. It is sort of like pi. Just a commonly used constant. It is part of the formula just like pi is when you write

  14. Mertsj
    • 4 years ago
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    \[A=\pi r^2\]

  15. Mertsj
    • 4 years ago
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    You don't replace pi with anything and you don't replace e with anything.

  16. anonymous
    • 4 years ago
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    can you help me figure out another problem but let me do it and maybe you can coach me.

  17. Mertsj
    • 4 years ago
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    It's numerical value (if you must know) is 2.718281828...

  18. Mertsj
    • 4 years ago
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    ok

  19. Mertsj
    • 4 years ago
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    Lay it on me.

  20. anonymous
    • 4 years ago
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    What rate of interest compounded continuously is needed for an investment of $500 to grow to $900 in 10 years?

  21. Mertsj
    • 4 years ago
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    What is A?

  22. anonymous
    • 4 years ago
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    900

  23. Mertsj
    • 4 years ago
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    What is P?

  24. anonymous
    • 4 years ago
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    500

  25. Mertsj
    • 4 years ago
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    What is t?

  26. anonymous
    • 4 years ago
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    10

  27. Mertsj
    • 4 years ago
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    What are you trying to find?

  28. anonymous
    • 4 years ago
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    the rate of interest

  29. Mertsj
    • 4 years ago
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    Yes. r

  30. Mertsj
    • 4 years ago
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    So plug everything in.

  31. anonymous
    • 4 years ago
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    900=500e^r10

  32. Mertsj
    • 4 years ago
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    \[900=500e ^{10r}\]

  33. Mertsj
    • 4 years ago
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    Divide both sides by 500

  34. anonymous
    • 4 years ago
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    ok

  35. anonymous
    • 4 years ago
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    In1.8=e^10r

  36. Mertsj
    • 4 years ago
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    \[1.8=e ^{10r}\]

  37. Mertsj
    • 4 years ago
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    Now when you take the natural log of both sides it should look like this: \[\ln 1.8=\ln e ^{10r}\]

  38. anonymous
    • 4 years ago
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    ok

  39. Mertsj
    • 4 years ago
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    Now bring the exponent down using the third law of logs and get this

  40. Mertsj
    • 4 years ago
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    \[\ln 1.8=10r \ln e\]

  41. Mertsj
    • 4 years ago
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    But of course ln e = 1 so we have:

  42. Mertsj
    • 4 years ago
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    \[\ln 1.8=10r\]

  43. Mertsj
    • 4 years ago
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    So just divide both sides by 10 and you are done

  44. anonymous
    • 4 years ago
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    0.18=r

  45. Mertsj
    • 4 years ago
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    \[\frac{\ln 1.8}{10}=r=.05878=5.88 %\]

  46. Mertsj
    • 4 years ago
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    Did you take the natural log of 1.8 before you divided by 10?

  47. anonymous
    • 4 years ago
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    no

  48. Mertsj
    • 4 years ago
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    Do you now how to do that?

  49. anonymous
    • 4 years ago
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    no

  50. Mertsj
    • 4 years ago
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    You do understand that it says ln 1.8 divided by 10?

  51. Mertsj
    • 4 years ago
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    Do you have a scientific calculator?

  52. anonymous
    • 4 years ago
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    yes

  53. Mertsj
    • 4 years ago
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    Can you find the ln button?

  54. Mertsj
    • 4 years ago
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    It's probably right next to the log button

  55. anonymous
    • 4 years ago
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    yes i just pressed it and got the same as you did do i now dive that by 10

  56. Mertsj
    • 4 years ago
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    Yes

  57. Mertsj
    • 4 years ago
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    Now multiply by 100 to change it to percent.

  58. anonymous
    • 4 years ago
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    got it you just answered my question!! thank you so much Mertsj

  59. Mertsj
    • 4 years ago
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    You're welcome and good luck. Isn't learning fun???!!!

  60. anonymous
    • 4 years ago
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    yeah your the best!!!!!

  61. Mertsj
    • 4 years ago
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    Thanks.

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