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?

Question

anonymous · Answer

Please help!! Will give a medal!!!

rainbow_rocks03 · Answer

plz help

anonymous · Answer

Do you know it? @rainbow_rocks03

rainbow_rocks03 · Answer

no sorry I don't

anonymous · Answer

Do the interest on on one whole year and then just multiply until you get 3000 or more and you'll find your answer.

anonymous · Answer

@PrincessRu    How do you do that? These are my answer choices. I think the third one is right. 
170.202 years 
14.3129 years 
171.755 years 
168.354 years

anonymous · Answer

Wait now I am getting A

anonymous · Answer

But I am not a 100% postive at all.

tkhunny · Answer

Can you do the first month?

anonymous · Answer

@tkhunny Would you do 100 times .02?

tkhunny · Answer

.02 = 2% and is an annual rate.  You need a monthly rate.

anonymous · Answer

So how do I do that? @tkhunny

tkhunny · Answer

You'll kick yourself.

0.02 / 12 = 0.00166666...

anonymous · Answer

hahaa! so then do I take that decimal and multipy it by something to get the years? @tkhunny

tkhunny · Answer

100 * 0.00166666 = 17¢

That's just the interest.  You need to accumulate all the interest and the initial deposit.

Annual Interest: 0.02
Monthly Interest: 0.02 / 12
Monthly Accumulation: 1 + (0.02 / 12)

You task is to see how long this takes to get to $3000

$100 [1 + (0.02/12)]^{n} = 3000$

Use your best logarithms to solve for 'n'.

anonymous · Answer

Wow I would have never gotten to that. I am not sure how to solve that. @tkhunny

anonymous · Answer

@tkhunny i got it to log29(.02/12)=n