Question

Can someone assist me with this problem please.

Answer 1

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)

Answer 2

plugin the values and see wat u get

Answer 3

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

Answer 4

yes ! give it to ur calculator

Answer 5

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

Answer 6

yes

Answer 7

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

Answer 8

yes

Answer 9

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

Answer 10

exponent first

Answer 11

\((1.0025)^{120}\)

Answer 12

269.87.. that seems like a small #

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

Yolanda 296.87?

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

I got 82,400

Answer 22

can you show your steps?

Answer 23

Fv= 2400 x (1+0.03)/0.03

Answer 24

that is not the formula. Look more carefully

Answer 25

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

Answer 26

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

Answer 27

27200?

Answer 28

ball park, but not exactly

what do you get for 1.03^10
?

Answer 29

then subtract 1

Answer 30

1.343916379

Answer 31

yes, now subtract 1 to get
.343916379

Answer 32

then 0.343916379

Answer 33

now divide by 0.03

Answer 34

27,513.31

Answer 35

yes, that looks good.

Answer 36

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

Answer 37

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

Answer 38

Wait so n= number of years?

Answer 39

n is the number of payments

Answer 40

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

Answer 41

yes

Answer 42

it doesnt say the number of payments

Answer 43

it says every month for 10 years

how many months in a year ?

Answer 44

n=120

Answer 45

yes

Answer 46

how do i figure out pymt
is
i= 0.03?

Answer 47

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

Answer 48

0.03/12?

Answer 49

yes

Answer 50

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

Answer 51

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

Answer 52

yeah im totally confused

Answer 53

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 ?

Answer 54

dont think so

Answer 55

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

Answer 56

0.03 ÷ 12?

Answer 57

yes

Answer 58

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

Answer 59

add 1

Answer 60

i= 5

Answer 61

just type into your calculator
0.03 ÷ 12 + 1
enter

Answer 62

you will get a number

now type
^
120

Answer 63

1.349353547

Answer 64

then type
-
1

(to subtract 1)

Answer 65

wait 1.0025+1= 2.0025

Answer 66

you are doing
1.0025^120 - 1

Answer 67

1.0025^120 - 1
you get
1.349353547 -1
and
.349353547

now divide by (0.03/12) (or 0.0025)

Answer 68

but what about the 0.349353547+1?

Answer 69

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)

Answer 70

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

Answer 71

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

Answer 72

whats the pymt?

Answer 73

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

Answer 74

200

Answer 75

yes

Answer 76

268.87

Answer 77

that doesnt seem right

Answer 78

because it is not correct.

you must use the correct formula

Answer 79

The FV?

Answer 80

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

Answer 81

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

Answer 82

you forgot the divide by i

Answer 83

1+0.03/12?

Answer 84

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)

Answer 85

oh i forgot to add divide by i

Answer 86

748.86

Answer 87

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

Answer 88

27948.28

Answer 89

yes

Answer 90

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