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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
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Hero @butterflydreamer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Use 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Try to fill in the formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@peachpi can you fill the formula for me? I am having trouble

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which variable/number are you having trouble with?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok. 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
 one year ago
Best ResponseYou've already chosen the best response.0A = 3000 P = 100 n = 12 right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what do you have so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[3000=100(1+\frac{ 1 }{ 12 })^{(12)t}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok. great. The only change is 1/12 should be 0.02/12 because the interest rate is 2%

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To solve it, start by dividing by the 100 and then simplifying the stuff in parentheses

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[30= (1.0016)^{(12)t}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, 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
 one year ago
Best ResponseYou've already chosen the best response.0To solve for t, divide by (12 ln 1.0016)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0if you have to round

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but it is not in the choices

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That'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
 one year ago
Best ResponseYou've already chosen the best response.0Throw a few more 6's on the 1.0016 and you'll come up with the first answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow thank you. this is complicated math.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You're welcome. yeah it is. And it's pretty messed up that 3 of the choices were so close together.
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