anonymous
  • anonymous
*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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@SolomonZelman
anonymous
  • anonymous
@Hero @butterflydreamer
anonymous
  • anonymous
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

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More answers

anonymous
  • anonymous
Try to fill in the formula
anonymous
  • anonymous
@peachpi can you fill the formula for me? I am having trouble
anonymous
  • anonymous
which variable/number are you having trouble with?
anonymous
  • anonymous
A, P, N
anonymous
  • anonymous
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?
anonymous
  • anonymous
A = 3000 P = 100 n = 12 right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
what do you have so far?
anonymous
  • anonymous
\[3000=100(1+\frac{ 1 }{ 12 })^{(12)t}\]
anonymous
  • anonymous
how would i find t
anonymous
  • anonymous
ok. great. The only change is 1/12 should be 0.02/12 because the interest rate is 2%
anonymous
  • anonymous
To solve it, start by dividing by the 100 and then simplifying the stuff in parentheses
anonymous
  • anonymous
\[30= (1.0016)^{(12)t}\]
anonymous
  • anonymous
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 \[\ln 30 = 12t \ln 1.0016\]
anonymous
  • anonymous
To solve for t, divide by (12 ln 1.0016)
anonymous
  • anonymous
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
anonymous
  • anonymous
if you have to round
anonymous
  • anonymous
did you get it?
anonymous
  • anonymous
I get 177.28737576
anonymous
  • anonymous
but it is not in the choices
anonymous
  • anonymous
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.
anonymous
  • anonymous
Throw a few more 6's on the 1.0016 and you'll come up with the first answer
anonymous
  • anonymous
Wow thank you. this is complicated math.
anonymous
  • anonymous
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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