anonymous
  • anonymous
Can someone assist me with this problem please.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
ganeshie8
  • 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)
ganeshie8
  • ganeshie8
plugin the values and see wat u get

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anonymous
  • anonymous
\[A= 200 (1+ \frac{ 0.03 }{ 12 }) ^{(12\times ^{10)}}\]
ganeshie8
  • ganeshie8
yes ! give it to ur calculator
anonymous
  • anonymous
So I do \[(1+0.03\div12)\]first?
ganeshie8
  • ganeshie8
yes
anonymous
  • anonymous
\[A= 200 (1 + 0.0025) ^{12\times10}\]
ganeshie8
  • ganeshie8
yes
anonymous
  • anonymous
\[A= 200(1.0025)^{(120)}\] I am unsure which part to do first.
ganeshie8
  • ganeshie8
exponent first
ganeshie8
  • ganeshie8
\((1.0025)^{120}\)
anonymous
  • anonymous
269.87.. that seems like a small #
phi
  • 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
ganeshie8
  • ganeshie8
thats all you wud get at 3% interest rate for 10 years this is not an annuity setup @phi
phi
  • 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
anonymous
  • anonymous
Yolanda 296.87?
phi
  • 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
ganeshie8
  • ganeshie8
yes @phi thanks for catching that, weird 260 is small i dint even notice... i need to go run an errand, cya
anonymous
  • anonymous
@phi so what is the equation set up now im officially confused could u write it step by step for me?
phi
  • phi
I wrote out Zach's can you do that one first ?
anonymous
  • anonymous
I got 82,400
phi
  • phi
can you show your steps?
anonymous
  • anonymous
Fv= 2400 x (1+0.03)/0.03
phi
  • phi
that is not the formula. Look more carefully
anonymous
  • anonymous
fv=2400 x (1+0.03)^(10)-1/0.03?
phi
  • phi
yes but use parens fv=2400 x ( (1+0.03)^(10)-1 ) /0.03?
anonymous
  • anonymous
27200?
phi
  • phi
ball park, but not exactly what do you get for 1.03^10 ?
phi
  • phi
then subtract 1
anonymous
  • anonymous
1.343916379
phi
  • phi
yes, now subtract 1 to get .343916379
anonymous
  • anonymous
then 0.343916379
phi
  • phi
now divide by 0.03
anonymous
  • anonymous
27,513.31
phi
  • phi
yes, that looks good.
anonymous
  • anonymous
So thats Zachs. now i have to find balance in Yolanda savings plan after 10 years
phi
  • 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
anonymous
  • anonymous
Wait so n= number of years?
phi
  • phi
n is the number of payments
anonymous
  • anonymous
FV= pymt \[\times (1+i)^n-1\]\[\div i\]
phi
  • phi
yes
anonymous
  • anonymous
it doesnt say the number of payments
phi
  • phi
it says every month for 10 years how many months in a year ?
anonymous
  • anonymous
n=120
phi
  • phi
yes
anonymous
  • anonymous
how do i figure out pymt is i= 0.03?
phi
  • phi
you want i per month. they give you the i for the whole year
anonymous
  • anonymous
0.03/12?
phi
  • phi
yes
anonymous
  • anonymous
Argh i hate this 2.5 x 10 ^ -03 how do i do that?
phi
  • 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
anonymous
  • anonymous
yeah im totally confused
phi
  • 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 ?
anonymous
  • anonymous
dont think so
phi
  • phi
type parens ( then 1 + 0.03/12 then close ) then ^ then 120
anonymous
  • anonymous
0.03 ÷ 12?
phi
  • phi
yes
anonymous
  • anonymous
2.5 x 10 ^ -03 how do i do that?
phi
  • phi
add 1
anonymous
  • anonymous
i= 5
phi
  • phi
just type into your calculator 0.03 ÷ 12 + 1 enter
phi
  • phi
you will get a number now type ^ 120
anonymous
  • anonymous
1.349353547
phi
  • phi
then type - 1 (to subtract 1)
anonymous
  • anonymous
wait 1.0025+1= 2.0025
phi
  • phi
you are doing 1.0025^120 - 1
phi
  • phi
1.0025^120 - 1 you get 1.349353547 -1 and .349353547 now divide by (0.03/12) (or 0.0025)
anonymous
  • anonymous
but what about the 0.349353547+1?
phi
  • 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)
anonymous
  • anonymous
it just FV= pymt (1.0025)^120 -1
phi
  • phi
you need parens and you need to divide by i \[ FV= pymt \cdot \frac{ (1+i)^n - 1}{i} \]
anonymous
  • anonymous
whats the pymt?
phi
  • phi
the payment is how much Yolanda is saving each month (how much she is paying into her bank account)
anonymous
  • anonymous
200
phi
  • phi
yes
anonymous
  • anonymous
268.87
anonymous
  • anonymous
that doesnt seem right
phi
  • phi
because it is not correct. you must use the correct formula
anonymous
  • anonymous
The FV?
phi
  • phi
yes \[ FV= pymt \cdot \frac{ (1+i)^n - 1}{i}\]
anonymous
  • anonymous
200 (1+0.03/12)^120-1
phi
  • phi
you forgot the divide by i
anonymous
  • anonymous
1+0.03/12?
phi
  • 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)
anonymous
  • anonymous
oh i forgot to add divide by i
anonymous
  • anonymous
748.86
phi
  • 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)=
anonymous
  • anonymous
27948.28
phi
  • phi
yes
anonymous
  • anonymous
and zach was what we did before which was 27,513.31
anonymous
  • anonymous

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