## 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

1. anonymous

@SolomonZelman

2. anonymous

@Hero @butterflydreamer

3. 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

4. anonymous

Try to fill in the formula

5. anonymous

@peachpi can you fill the formula for me? I am having trouble

6. anonymous

which variable/number are you having trouble with?

7. anonymous

A, P, N

8. 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?

9. anonymous

A = 3000 P = 100 n = 12 right?

10. anonymous

yes

11. anonymous

what do you have so far?

12. anonymous

$3000=100(1+\frac{ 1 }{ 12 })^{(12)t}$

13. anonymous

how would i find t

14. anonymous

ok. great. The only change is 1/12 should be 0.02/12 because the interest rate is 2%

15. anonymous

To solve it, start by dividing by the 100 and then simplifying the stuff in parentheses

16. anonymous

$30= (1.0016)^{(12)t}$

17. 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 $\ln 30 = 12t \ln 1.0016$

18. anonymous

To solve for t, divide by (12 ln 1.0016)

19. 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

20. anonymous

if you have to round

21. anonymous

did you get it?

22. anonymous

I get 177.28737576

23. anonymous

but it is not in the choices

24. 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.

25. anonymous

Throw a few more 6's on the 1.0016 and you'll come up with the first answer

26. anonymous

Wow thank you. this is complicated math.

27. anonymous

You're welcome. yeah it is. And it's pretty messed up that 3 of the choices were so close together.