## anonymous one year ago 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? • This Question is Closed 1. anonymous @ospreytriple 2. anonymous @Mertsj 3. anonymous Do you know the compound interest formula from your course? 4. anonymous yeah 5. anonymous a(t)=p(1+r)^t 6. anonymous 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?

7. anonymous

100

8. anonymous

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.

9. anonymous

\$100 is correct.

10. anonymous

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?

11. anonymous

ummm 12??

12. anonymous

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

13. anonymous

I agree

14. anonymous

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

15. anonymous

0.02

16. anonymous

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

17. anonymous

ok so 0.02/12 ??

18. Mertsj

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

19. Mertsj

Solve for t

20. anonymous

That's it. What's r then?

21. anonymous

3000=100.16667)^12t

22. anonymous

r is not 0.16667. Try it again

23. anonymous

r=0.02

24. anonymous

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

25. anonymous

0.001666667

26. anonymous

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

27. Mertsj

r=.02

28. anonymous

Perhaps you'd like to take over @Mertsj

29. anonymous

3000=(100.16667)^12t

30. anonymous

What's 100 + 0.0016667 ?

31. Mertsj

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

32. anonymous

100.0016667

33. anonymous

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

34. anonymous

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

35. Mertsj

$300=(1.01666666)^{12t}$

36. anonymous

ok so 1og 300=....?

37. Mertsj

$\log_{10}300=12t \log_{10}1.0166666666$

38. anonymous

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

39. Mertsj

$\frac{\log_{10}300}{\log_{10}1.016666666}=12t$

40. anonymous

ok hold onn

41. anonymous

300/ 1.01666666=12t

42. Mertsj

$345.07=12t$

43. anonymous

28. 76

44. Mertsj

$28.8=t$

45. anonymous

170.202 years 14.3129 years 171.755 years 168.354 years

46. anonymous

47. anonymous

@heretohelpalways @ganeshie8

48. Mertsj

Error: 3000/100=30

49. anonymous

yes

50. Mertsj

$\frac{\log_{10}30}{\log_{10}1.0166666666}=12t$

51. anonymous

ok so 30/1.016666

52. anonymous

29.5081967232=12t

53. Mertsj

you have to take the log of those numbers.

54. anonymous

so log 29.508...?

55. Mertsj

Do you see that it says log 30?

56. anonymous

1.46994267012

57. anonymous

1.47712125472 i mean

58. anonymous

would 168.354 years be the answer?

59. Mertsj

I keep getting 17.14

60. anonymous

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

61. anonymous

Oh well, let's call it a day loll

62. anonymous

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

63. Mertsj

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

64. Mertsj

$\frac{\log_{10}30}{\log_{10}1.00166666666666}=12t$

65. Mertsj

$2042.4185=12t$

66. Mertsj

$170.20=t$