*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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*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
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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

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Other answers:

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