Question

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?

Answer 1

@ospreytriple

Answer 2

@Mertsj

Answer 3

Do you know the compound interest formula from your course?

Answer 4

yeah

Answer 5

a(t)=p(1+r)^t

Answer 6

OK. It looks like we want a(t) to be $3000 cause that's how much needs to be saved. p is the present value. How much is that?

Answer 7

100

Answer 8

OH!! In your previous question, the right hand side of the equation was NEGATIVE, so the correct answer is the negative number. Sorry about that.

Answer 9

$100 is correct.

Answer 10

The interest rate (r) is a little bit tricky. The question says the nominal yearly interest rate is 2% but it is compounded monthly. Do you know how to get the interest rate in this case?

Answer 11

ummm 12??

Answer 12

Well, it's 2% per year, but for a month it's going to be 1/12 as much. What do you think?

Answer 13

I agree

Answer 14

OK. so r = 2% /12. Have to convert that to a decimal. What do you get?

Answer 15

0.02

Answer 16

Right. But you still have to divide by 12 to get r.

Answer 17

ok so 0.02/12 ??

Answer 18

\[A=P(1+\frac{r}{n})^{nt}\]
\[3000=100(1+\frac{.02}{12})^{12t}\]

Answer 19

Solve for t

Answer 20

That's it. What's r then?

Answer 21

3000=100.16667)^12t

Answer 22

r is not 0.16667. Try it again

Answer 23

r=0.02

Answer 24

Remember, we already established that r = 0.02/12. What do you get?

Answer 25

0.001666667

Answer 26

Great. Now out that value of r into the compound interest formula and what do you get?

Answer 27

r=.02

Answer 28

Perhaps you'd like to take over @Mertsj

Answer 29

3000=(100.16667)^12t

Answer 30

What's 100 + 0.0016667 ?

Answer 31

Continuing:
\[\frac{3000}{100}=\frac{100(1+\frac{.02}{12})^{12t}}{100}\]

Answer 32

100.0016667

Answer 33

30=(1+0.02/12)^12t

Answer 34

Great. So you have\[3000 = 100.0016667^{12t}\]Now take the log of both sides

Answer 35

\[300=(1.01666666)^{12t}\]

Answer 36

ok so 1og 300=....?

Answer 37

\[\log_{10}300=12t \log_{10}1.0166666666 \]

Answer 38

I'm sorry @BellaBlue77 . Our work is being hijacked. I'm out. Good luck.

Answer 39

\[\frac{\log_{10}300}{\log_{10}1.016666666}=12t \]

Answer 40

ok hold onn

Answer 41

300/ 1.01666666=12t

Answer 42

\[345.07=12t\]

Answer 43

28. 76

Answer 44

\[28.8=t\]

Answer 45

170.202 years
14.3129 years
171.755 years
168.354 years

Answer 46

That's not an answer choice

Answer 47

@heretohelpalways @ganeshie8

Answer 48

Error: 3000/100=30

Answer 49

yes

Answer 50

\[\frac{\log_{10}30}{\log_{10}1.0166666666}=12t \]

Answer 51

ok so 30/1.016666

Answer 52

29.5081967232=12t

Answer 53

you have to take the log of those numbers.

Answer 54

so log 29.508...?

Answer 55

Do you see that it says log 30?

Answer 56

1.46994267012

Answer 57

1.47712125472 i mean

Answer 58

would 168.354 years be the answer?

Answer 59

I keep getting 17.14

Answer 60

I know :( But thats not an answer choice.
170.202 years
14.3129 years
171.755 years
168.354 years
see?

Answer 61

Oh well, let's call it a day loll

Answer 62

If you find the answer, message me pleae, I'll be back tommorw

Answer 63

Starting over:
\[3000=100(1+\frac{.02}{12})^{12t}\]
\[30=(1+.00166666666)^{12t}\]

Answer 64

\[\frac{\log_{10}30}{\log_{10}1.00166666666666}=12t \]

Answer 65

\[2042.4185=12t\]

Answer 66

\[170.20=t\]