Can someone assist me with this problem please.
 anonymous
Can someone assist me with this problem please.
 katieb
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 anonymous
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 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
plugin the values and see wat u get
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 anonymous
\[A= 200 (1+ \frac{ 0.03 }{ 12 }) ^{(12\times ^{10)}}\]
 ganeshie8
yes ! give it to ur calculator
 anonymous
So I do \[(1+0.03\div12)\]first?
 ganeshie8
yes
 anonymous
\[A= 200 (1 + 0.0025) ^{12\times10}\]
 ganeshie8
yes
 anonymous
\[A= 200(1.0025)^{(120)}\] I am unsure which part to do first.
 ganeshie8
exponent first
 ganeshie8
\((1.0025)^{120}\)
 anonymous
269.87.. that seems like a small #
 phi
You should be using the formula that gives you the future value of a stream of regular payments.
see http://www.annuityformulas.org/futurevalueofregularpayments.html
 ganeshie8
thats all you wud get at 3% interest rate for 10 years
this is not an annuity setup @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
Yolanda 296.87?
 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
yes @phi thanks for catching that, weird 260 is small i dint even notice... i need to go run an errand, cya
 anonymous
@phi so what is the equation set up now im officially confused could u write it step by step for me?
 phi
I wrote out Zach's can you do that one first ?
 anonymous
I got 82,400
 phi
can you show your steps?
 anonymous
Fv= 2400 x (1+0.03)/0.03
 phi
that is not the formula. Look more carefully
 anonymous
fv=2400 x (1+0.03)^(10)1/0.03?
 phi
yes but use parens
fv=2400 x ( (1+0.03)^(10)1 ) /0.03?
 anonymous
27200?
 phi
ball park, but not exactly
what do you get for 1.03^10
?
 phi
then subtract 1
 anonymous
1.343916379
 phi
yes, now subtract 1 to get
.343916379
 anonymous
then 0.343916379
 phi
now divide by 0.03
 anonymous
27,513.31
 phi
yes, that looks good.
 anonymous
So thats Zachs. now i have to find balance in Yolanda savings plan after 10 years
 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
Wait so n= number of years?
 phi
n is the number of payments
 anonymous
FV= pymt \[\times (1+i)^n1\]\[\div i\]
 phi
yes
 anonymous
it doesnt say the number of payments
 phi
it says every month for 10 years
how many months in a year ?
 anonymous
n=120
 phi
yes
 anonymous
how do i figure out pymt
is
i= 0.03?
 phi
you want i per month. they give you the i for the whole year
 anonymous
0.03/12?
 phi
yes
 anonymous
Argh i hate this 2.5 x 10 ^ 03 how do i do that?
 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
yeah im totally confused
 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
dont think so
 phi
type parens
(
then 1 + 0.03/12
then close
)
then
^
then 120
 anonymous
0.03 Ã· 12?
 phi
yes
 anonymous
2.5 x 10 ^ 03 how do i do that?
 phi
add 1
 anonymous
i= 5
 phi
just type into your calculator
0.03 Ã· 12 + 1
enter
 phi
you will get a number
now type
^
120
 anonymous
1.349353547
 phi
then type

1
(to subtract 1)
 anonymous
wait 1.0025+1= 2.0025
 phi
you are doing
1.0025^120  1
 phi
1.0025^120  1
you get
1.349353547 1
and
.349353547
now divide by (0.03/12) (or 0.0025)
 anonymous
but what about the 0.349353547+1?
 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
it just FV= pymt (1.0025)^120 1
 phi
you need parens and you need to divide by i
\[ FV= pymt \cdot \frac{ (1+i)^n  1}{i} \]
 anonymous
whats the pymt?
 phi
the payment is how much Yolanda is saving each month (how much she is paying into her bank account)
 anonymous
200
 phi
yes
 anonymous
268.87
 anonymous
that doesnt seem right
 phi
because it is not correct.
you must use the correct formula
 anonymous
The FV?
 phi
yes
\[ FV= pymt \cdot \frac{ (1+i)^n  1}{i}\]
 anonymous
200 (1+0.03/12)^1201
 phi
you forgot the divide by i
 anonymous
1+0.03/12?
 phi
I am saying that this is not correct
200 (1+0.03/12)^1201
the correct formula is
200 ( (1+0.03/12)^1201)/ (0.03/12)
 anonymous
oh i forgot to add divide by i
 anonymous
748.86
 phi
you are not doing the calculation correctly
type this into the google search window
200 * ( (1+0.03/12)^1201)/ (0.03/12)=
 anonymous
27948.28
 phi
yes
 anonymous
and zach was what we did before which was 27,513.31
 anonymous
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