## nslesin 2 years ago Can someone assist me with this problem please.

1. nslesin

2. ganeshie8

use the compound interest formula $$\large A = P(1+\frac{r}{n})^{nt}$$ $$P$$ = 200 $$r$$ = 3% = 0.03 $$n$$ = 12 (months) $$t$$ = 10 (years)

3. ganeshie8

plugin the values and see wat u get

4. nslesin

$A= 200 (1+ \frac{ 0.03 }{ 12 }) ^{(12\times ^{10)}}$

5. ganeshie8

yes ! give it to ur calculator

6. nslesin

So I do $(1+0.03\div12)$first?

7. ganeshie8

yes

8. nslesin

$A= 200 (1 + 0.0025) ^{12\times10}$

9. ganeshie8

yes

10. nslesin

$A= 200(1.0025)^{(120)}$ I am unsure which part to do first.

11. ganeshie8

exponent first

12. ganeshie8

$$(1.0025)^{120}$$

13. nslesin

269.87.. that seems like a small #

14. phi

You should be using the formula that gives you the future value of a stream of regular payments. see http://www.annuityformulas.org/future-value-of-regular-payments.html

15. ganeshie8

thats all you wud get at 3% interest rate for 10 years this is not an annuity setup @phi

16. phi

For Zach, the equation is $FV= pymt \cdot \frac{ (1+i)^n - 1}{i}$ where n is 10 years, pymt is 2400 and i is 0.03

17. nslesin

Yolanda 296.87?

18. phi

no, Yolanda is depositing 200 per month, or 200*12= 2400 per year for 10 years = 24,000 that is if there was no interest. But there is 3% interest, so it will be bigger than that

19. ganeshie8

yes @phi thanks for catching that, weird 260 is small i dint even notice... i need to go run an errand, cya

20. nslesin

@phi so what is the equation set up now im officially confused could u write it step by step for me?

21. phi

I wrote out Zach's can you do that one first ?

22. nslesin

I got 82,400

23. phi

24. nslesin

Fv= 2400 x (1+0.03)/0.03

25. phi

that is not the formula. Look more carefully

26. nslesin

fv=2400 x (1+0.03)^(10)-1/0.03?

27. phi

yes but use parens fv=2400 x ( (1+0.03)^(10)-1 ) /0.03?

28. nslesin

27200?

29. phi

ball park, but not exactly what do you get for 1.03^10 ?

30. phi

then subtract 1

31. nslesin

1.343916379

32. phi

yes, now subtract 1 to get .343916379

33. nslesin

then 0.343916379

34. phi

now divide by 0.03

35. nslesin

27,513.31

36. phi

yes, that looks good.

37. nslesin

So thats Zachs. now i have to find balance in Yolanda savings plan after 10 years

38. phi

For Yolanda you use the same formula (they don't say if she deposits the \$200 at the end of each month.. but let's assume she does) however, n is in months (so 10*12= 120) and the interest is per month so 0.03/12

39. nslesin

Wait so n= number of years?

40. phi

n is the number of payments

41. nslesin

FV= pymt $\times (1+i)^n-1$$\div i$

42. phi

yes

43. nslesin

it doesnt say the number of payments

44. phi

it says every month for 10 years how many months in a year ?

45. nslesin

n=120

46. phi

yes

47. nslesin

how do i figure out pymt is i= 0.03?

48. phi

you want i per month. they give you the i for the whole year

49. nslesin

0.03/12?

50. phi

yes

51. nslesin

Argh i hate this 2.5 x 10 ^ -03 how do i do that?

52. phi

you want (1+i)^120 where i= 0.03/12 so do it in steps: 0.03/12 add 1 raise to the 120 power

53. nslesin

yeah im totally confused

54. phi

you are doing $FV= pymt \cdot \frac{ (1+i)^n - 1}{i}$ does your calculator have memory, so you can put 0.03/12 into memory ?

55. nslesin

dont think so

56. phi

type parens ( then 1 + 0.03/12 then close ) then ^ then 120

57. nslesin

0.03 ÷ 12?

58. phi

yes

59. nslesin

2.5 x 10 ^ -03 how do i do that?

60. phi

61. nslesin

i= 5

62. phi

just type into your calculator 0.03 ÷ 12 + 1 enter

63. phi

you will get a number now type ^ 120

64. nslesin

1.349353547

65. phi

then type - 1 (to subtract 1)

66. nslesin

wait 1.0025+1= 2.0025

67. phi

you are doing 1.0025^120 - 1

68. phi

1.0025^120 - 1 you get 1.349353547 -1 and .349353547 now divide by (0.03/12) (or 0.0025)

69. nslesin

70. phi

you are doing 1.0025^120 - 1 which gives you 0.349353547 at this point, you do not add +1. the formula says divide by i i is 0.0025 (the same as 0.03/12)

71. nslesin

it just FV= pymt (1.0025)^120 -1

72. phi

you need parens and you need to divide by i $FV= pymt \cdot \frac{ (1+i)^n - 1}{i}$

73. nslesin

whats the pymt?

74. phi

the payment is how much Yolanda is saving each month (how much she is paying into her bank account)

75. nslesin

200

76. phi

yes

77. nslesin

268.87

78. nslesin

that doesnt seem right

79. phi

because it is not correct. you must use the correct formula

80. nslesin

The FV?

81. phi

yes $FV= pymt \cdot \frac{ (1+i)^n - 1}{i}$

82. nslesin

200 (1+0.03/12)^120-1

83. phi

you forgot the divide by i

84. nslesin

1+0.03/12?

85. phi

I am saying that this is not correct 200 (1+0.03/12)^120-1 the correct formula is 200 ( (1+0.03/12)^120-1)/ (0.03/12)

86. nslesin

oh i forgot to add divide by i

87. nslesin

748.86

88. phi

you are not doing the calculation correctly type this into the google search window 200 * ( (1+0.03/12)^120-1)/ (0.03/12)=

89. nslesin

27948.28

90. phi

yes

91. nslesin

and zach was what we did before which was 27,513.31

92. nslesin