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anonymous

  • one year ago

*I need HELP* 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? 170.202 years 14.3129 years 171.755 years 168.354 years

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  1. anonymous
    • one year ago
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    @SolomonZelman

  2. anonymous
    • one year ago
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    @Hero @butterflydreamer

  3. anonymous
    • one year ago
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    Use the compound interest formula \[A=P(1+\frac{ r }{ n })^{nt}\] A = final amount P = initial amount r = interest rate as a decimal n = number of times interest is compounded in a year t = number of years → what you're trying to find

  4. anonymous
    • one year ago
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    Try to fill in the formula

  5. anonymous
    • one year ago
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    @peachpi can you fill the formula for me? I am having trouble

  6. anonymous
    • one year ago
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    which variable/number are you having trouble with?

  7. anonymous
    • one year ago
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    A, P, N

  8. anonymous
    • one year ago
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    ok. These are all in the question. For A, what is the amount they're trying to save? For P, what is the amount that was deposited? For n, how often is the interest compounded?

  9. anonymous
    • one year ago
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    A = 3000 P = 100 n = 12 right?

  10. anonymous
    • one year ago
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    yes

  11. anonymous
    • one year ago
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    what do you have so far?

  12. anonymous
    • one year ago
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    \[3000=100(1+\frac{ 1 }{ 12 })^{(12)t}\]

  13. anonymous
    • one year ago
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    how would i find t

  14. anonymous
    • one year ago
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    ok. great. The only change is 1/12 should be 0.02/12 because the interest rate is 2%

  15. anonymous
    • one year ago
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    To solve it, start by dividing by the 100 and then simplifying the stuff in parentheses

  16. anonymous
    • one year ago
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    \[30= (1.0016)^{(12)t}\]

  17. anonymous
    • one year ago
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    yes, so now you want to take the natural log (ln) of both sides. \[\ln 30=\ln (1.0016)^{12t}\] and apply the rule \[\ln a^b = b \ln a\] to get \[\ln 30 = 12t \ln 1.0016\]

  18. anonymous
    • one year ago
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    To solve for t, divide by (12 ln 1.0016)

  19. anonymous
    • one year ago
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    I know you rounded (1 + 0.02/12) to 1.0016 for the sake of writing it down, but you really don't want to round these problems until the end. It can mess up your answer. More digits is better

  20. anonymous
    • one year ago
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    if you have to round

  21. anonymous
    • one year ago
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    did you get it?

  22. anonymous
    • one year ago
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    I get 177.28737576

  23. anonymous
    • one year ago
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    but it is not in the choices

  24. anonymous
    • one year ago
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    That's the rounding error I mentioned above. You should use the exact answer for the stuff in parentheses (1 + .02/12) = 601/600 as a fraction, but you can usually get away with 8 to 10 numbers after the decimal point.

  25. anonymous
    • one year ago
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    Throw a few more 6's on the 1.0016 and you'll come up with the first answer

  26. anonymous
    • one year ago
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    Wow thank you. this is complicated math.

  27. anonymous
    • one year ago
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    You're welcome. yeah it is. And it's pretty messed up that 3 of the choices were so close together.

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