Questions on Algebra in Finance answered by real tutors!

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in order for you to get the money forever, you have to invest enough so that the principal never gets below a minimum figure.
---
what you will be drawing out each year is 8000.
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assume that you are starting in the 4th year.
your interest rate is 10% forever.
your money that you want to take out each year is $8,000
your equation would be:
p = principal
r = interest rate
i = interest
---
p*r = i
solving for p, we get:
p = i/r
if i = 8000 and r = .1, then p = 8000/.1 = 80000
---
to see if this is true, then check to see if this holds.
80000 * .1 = 8000 + 80000 = 88000 at the end of the 4th year.
withdraw 8000 and you are left with 80000.
80000 * .1 = 8000 + 80000 = 88000 at the end of the 5th year.
withdraw 8000 and you are left with 80000.
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it's plain to see that if you have 80000 at the beginning of the 4th year you can withdraw 8000 forever assuming the interest rate remains at 10%.
----
now to the first 3 years.
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you need to have 80,000 left in the account at the beginning of the 4th year.
your future value is therefore 80,000
you need to withdraw 8000 each year.
your interest rate is .08 per year.
your initial investment is x (unknown)
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this winds up being the future value of an annuity formula.
that formula is so complicated i won't even show it here.
i used the PV formula from excel.
that function takes in arguments as follows:
PV(rate,nper,pmt,fv,type)
where:
rate is the interest rate per payment period = .08 per year.
nper is number of payment periods = 3 years
pmt is 8000 which is the amount you withdraw each period.
fv is future value of the investment = 80,000 cause that's what you need to have at the end of the 3 years.
type is 0 which means the payments are made at the end of each payment period.
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that function gave me the answer.
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the answer is:
initial investment is 84,123.36
---
here's how it works:
---
the problem:
How much you should invest now to get $8,000 annually for ever, given an interest rate of 8% for the first 3 years & 10% for the remaining years
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the answer:
you invest 84,123.36 now.
----
interest rate for the first 3 years is 8% annually.
amount to withdraw each year is 8,000
---
end of year 1:
1.08 * 84123.36 - 8000 = 82853.2288
end of year 2:
1.08 * 82853.2288 - 8000 = 81481.4871
end of year 3:
1.08 * 81481.4871 - 8000 = 80000.00607
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now you start at 10% a year interest:
---
end of year 4:
1.10 * 80000.00607 - 8000 = 80,000.00668
end of year 5:
1.10 * 80000.00668 - 8000 = 80,000.00735
etc.........
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you will be able to withdraw 8000 forever and the principal will remain the same.
---
there is a very slight increase of principal each year due to rounding errors.
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hope this helps.
i tried deriving the formula for the first 3 years but gave up because it was too complicated and was taking too much time.
for problems like this, using a financial calculator, or microsoft excel financial functions, is the best way to go.
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i'm not an accounting student but i would say that the amount of cash received would be 30,500.
here's why:
AR1 = accounts receivable at the start.
AR2 = accounts receivable at the finish.
C = cash
CRS = credit sales
---
general formula should be:
AR2 = AR1 + CRS - C
---
AR1 = 13,500
AR2 = 5,000
CRS = 22,000
C = unknown at this time.
---
substituting in the formula, we get:
5,000 = 13,500 + 22,000 - C
combining like terms we get:
5,000 = 35,500 - C
adding C to both sides of the equation we get:
C + 5,000 = 35,500
subtracting 5,000 from both sides we get:
C = 35,500 - 5,000 = 30,500
---
looks like cash = $30,500
that would be answer c.
---

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i would have to say $30.00
here's why:
1300 whole units
400 units 50% completed = 200 equivalent whole units since 200 * 1 = 400 * .5
total equivalent whole units is 1300 + 200 = 1500.
45000 / 1500 = 30
cost per equivalent whole unit is $30.00
---

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total material is 12000 + 15000 = 27000
total direct labor is 24000 + 45000 = 69000
total overhead is .8 * 69000 = 55200
total cost for the job is 27000 + 69000 + 55200 = 151200

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problem number 1:
---
let x = first negative integer
let x + 1 = second negative integer.
---
the problem states that the square of the larger minus 5 times the smaller is equal to 71.
---
this means that
(x+1)^2 - 5x = 71
which means that
x^2 + 2x + 1 - 5x = 71
which means that
x^2 - 3x + 1 = 71
which means that
x^2 - 3x - 70 = 0
which means that
(x-10) * (x+7) = 0
which means that
x = 10
or
x = -7
---
since the number is negative, x = -7 is the only applicable answer.
---
to prove, substitute in original equation.
---
the numbers are x and x+1 which means that the numbers are -7 and -6.
-6 is the larger number.
square of the larger number minus 5 times the smaller number is 71.
(-6)^2 - (5*(-7)) = 36 - (-35) = 36 + 35 = 71.
---
x = -7 checks out ok.
---
answer is the 2 negative consecutive numbers are -7 and -6.
---
problem number 2:
---
let x = one of the negative numbers,
then x + 2 = next negative number, and x + 4 = next negative number.
---
largest negative number is x + 4
middle negative number is x + 2
smallest negative number is x
---
problem states that the square of the middle negative number is greater than the largest negative number by 10.
this means that (x+2)^2 = (x+4) + 10
which means that
x^2 + 4x + 4 = x + 14
which means that
x^2 + 3x - 10 = 0
which means that
(x+5) * (x-2) = 0
which means that
x = -5
or
x = 2
---
since the number has to be negative, then x = -5 is the only applicable answer to the problem.
---
if x = -5, then
x + 2 = -3, and
x + 4 = -1
---
largest number is -1
middle number is -3
---
square of second number is 9
largest number + 10 is 9
square of second number equals the largest number plus 10 which satisfies the problem statement.
---
answer is the 3 negative consecutive numbers are:
-5, -3, -1
---

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These formulas are cumbersome to calculate on paper. You would be better served
if you use a calc like a Ti83, financial application. With this you can enter
and combination of interest rate, loan amt, no. of payments, payment amt and
immediately determine what you want to know.
:
For instance if you have loan of 415,000 with an interest rate of 5%, and the
monthly payment has to be 2362, enter these values and and find the number
payments required to pay it off. About 317 payments or about 26 yrs. Or any
other combination of interest, payment amt, time, etc can be easily determined.
:
With practice you can find out anything you want about a mortgage in minutes

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Your grades on five math tests are 95,86,79,88,83. What grade do you need on the sixth test to have an average of 90%.
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Let the grade on the 6th test be "x".
EQUATION:
(95+86+79+88 + 83 + x)/6 = 90
431 + x = 540
x = 109
-----------
You would need a grade of 109 on the 6th test.
Cheers,
Stan H.

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To score an average of 90, you need 90*6 = 540 points.
So far you have 95 + 86 + 79 + 88 + 83 = 431 points.
You would need 540 - 431 = 109 points which is only possibly if the teacher gives a bonus question!

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3.25 hrs is 3 hrs and 15 min.
3 hrs after 1:20 AM is 4:20 AM
Another 15 min makes it 4:35 AM naswer

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The problem can be solved by going back to basic principles. Each cash flow is discounted back to the date of the computation by multiplying the cash flow by (1/(1+rate of return))^(number of years from the date of the computation to the date of payment.
So the discounted cash flows are:
3000*(1/1.1)^1
3000*(1/1.1)^2
3000*(1/1.1)^3
3000*(1/1.1)^4
The four discounted cash flows are added together
3000*(1/1.1)^2 + 3000*(1/1.1)^2 + 3000*(1/1.1)^3 + 3000*(1.1)^4
= 3000
The sum of the 4 numbers in the brackets is called an annuity immediate. There is a formula for annuity immediates and can be easily calculated. This approach works because the cash flow each year is level. Otherwise, the basic principle's approach always works.
Larry

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We have to get d on one side and everything else on the other.
(5 / 1.045) + [ 105 / (1 + d2)^2 ]=100
105/(1+d^2)^2=100-(5/1.045)
=(104.5-5)/1.045
=99.5/1.045
(1+d^2)^2/105=1.045/99.5
(1+d^2)^2=105*1.045/99.5
=1.027963819...
1+d^2=sqrt(1.027963819...)
=1.050125621
d^2=1.050125621... -1
=0.050125621...
d=sqrt(0.050125621...)
=0.2238875178...
.
Ed

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the answer would be c.
:
ROI=net operating income/avg operating assets
:
.12=x/375000
:

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the answer would be c.
:
ROI=net operating income/avg operating assets
:
.12=x/375000
:

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both A and C are backed and insured
:
Bendix is owned by Honeywell corp who is highly diversified
:
whereas Southwest airlines is not very diversified and the airlines are VERY risky to own.
:
I would pick Southwest Airlines as the highest RISK based on current information.
:
I dont believe that either the bonds with southwest or the commercial paper with Bendix is secured....so this would be based on that premise

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.12*60,000=$7,200 IS THE TOTAL RETURN ON INVESTMENT.
SALES +.04SALES=7,200
1.04SALES=7,200
SALES=7,200/1.04
SALES=$=6,923.08 WAS THE INCREASE IN SALES.
.04*6,923.08=276.92 INCREASE IN INCOME.
PROOF:
6,923.08+276.92=$7,200

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According to the simple interest formula I= Prt, in this problem, the Interest is the inflow which is $9000 PER YEAR, which means that the Time is 1 year, and the principle is $48000

I = Prt
9000= 48000*r*1

Divide boths sides by 48000 (got a calculator??):

%, which is greater than the desired rate of return!! Pretty good investment, considering my bank pays less than 1% on savings accounts!!

R^2

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The operating assets are the investment.
800000*.08=64,000
64000/500000=.128=12.8%
.
Ed

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job 1(2 hours)
job 2(10 hours)
:
total hours 12
:
percentage of job 2 hours to total hours:
:
10/12
:
overhead cost assigned to job 2:: 10/12(6000)=5000
:
answer is D

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If they continue to outsource the item, their total cost will be 5,000 X $20.

If they make the switches themselves, then it will cost:

$3 + $2 + $1 = $6 per switch times 5000 switches PLUS

$25,000 batch set-up PLUS

$37,500 salaries PLUS

$20,000 factory cost PLUS

$1,500 times 12 months lost lease revenue.

Add up all of the costs to make the switches themselves and compare it to the total cost of continuing to outsource. You can do your own arithmetic.

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Unit selling price: Canister Bag = $250 ; Tote Bag = $120
Unit variable cost: Canister Bag = $110 ; Tote Bag = $80
Number of units produced and sold: Canister Bag = 6,000 ; Tote Bag = 4,000
:
sales-v.costs=contribution margin
:
cm-fixed costs=zero for breakeven
:
cm-280000=0
:
cm=280000
let x and y be the number of units of the canister and tote bags respectively
:
sales-v.costs=contribution margin(cm)
:
250x-110x+120y-80y=280000
:
140x+40y=280000.....eq 1
:
ratio of --->6000y=4000x--->y=4000x/6000=2x/3....eq 2
:
take y's value eq 2 and plug it into eq 1
:
140x+40(2x/3)=280000
:
140x+80x/3=280000
:
420x+80x=840000
:
500x=840000
:


:
so total units to break even is 1680+1120=2800 units
:
answer is C

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To compute the break-even point for a company:
Sales – Variable Costs = Contribution Margin
Contribution Margin – Fixed Costs = Net Income (which should be 0 to calculate the break-even point
:
contribution margin -15000 must equal zero
:
CM-15000=0......so CM=15000
:
we are working backward here so now
:
Sales(S)-VC=CM(15000)
lets call the number of standard units sold x
lets call the number of premium units sold y
Sales-VC(standard)+Sales-VC(premium)=15000
:
100x-75x+150y-100y=15000
:
25x+50y=15000.....eq 1
:
according to the sales mix ration of x to y is $1000 to $2000
:

:
1000y=2000x--->x=1/2y.....eq 2
:
take x's value from eq 2 and plug it into eq 1
:
25(y/2)+50y=15000
:
25y+100y=30000... multiplied all terms by 2
:
125y=30000
:
y=240
:
x=1/2(240)=120
:
so to figure out total sales
:
to break even
:
C is your answer

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B - $24,000 - Since there are 24 activities (set-ups) and since time is not given so we can assume it takes the same amount of time to do each set-up, each set-up costs $2,000. Since each type of production (steel and titanium) has 12 set-up, $2,000 time 12 = $24,000.
Under unit based accounting, which is what most companies still do, the titanium cost would have been $9,600 (20% of the total set-up cost, since 20% or output was titanium handle bars). This of course would have been overcharging steel handle bar production since since in reality, half the costs should be allocated to the 1/2 the set-ups for titanium handle bars.

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No, we aren't going to do your entire homework assignment.

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If you have specific questions about how to do this, ask them. But don't expect us to do your entire assignment for you. That is not the purpose of this site, and expecting us to do that is misuse.

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http://regentsprep.org/Regents/math/orderop/Lorder.htm

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lets call the amount invested in account 1, x and in account 2, y=(8400-x).
:
account 1-----> .0825(x)
:
account 2-----> .05(8480-x)
:
we set these two formula's equal to each other to determine the amounts at which account 1 and account 2 will be equal.
:
.0825x=.05(8480-x)
:
.0825x=424-.05x
:
.1325x=424
:
amount invested at 8.25%
:
amount invested at 5%

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The Pacific investment group invested some money in a certificate of deposit (cd) that earns 6.5% annual simple interest.
Twice the amount at 6.5% was invested an a 2nd cd that earns 8.5% annual simple interest.
If a total annual interest earned from 2 investments $5875.00 How much was invested at 6.5%. How much was deposited in the certificate of deposit?
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Let "x" be amount invested at 6.5%; Interest = 0.065x dollars
-------------------------
Then "2x" is amt. invested at 8.5%: Interest = 0.085(2x)= 0.17x dollars
-------------------------
EQUATION:
interest + interest = 5875 dollars
0.065x + 0.17x = 5875
0.235x = 5875
x = $25000 dollars (amt invested at 6.5%)
-----------
2x = $50,000 (amt.invested at 8.5%)
======================================
Cheers,
Stan H.

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A chemist has 2 alloys, 1 of which is 10% gold and 20% lead, and the other of which is 30% gold anf 35% lead. How many grams of each of the 2 alloys should be used to make an alloy that contains 63g of gold and 111g of lead?
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Gold Equation: 0.10x + 0.30y = 63
Lead Equation: 0.20x + 0.35y = 111
-----------------------------------------
Use whatever method you know to solve this system to get:
x = 450 grams (amt of the 1st alloy in the final mixture)
y = 60 grams (amt of the 2nd alloy in the final mixture)
============================================================
Cheers,
Stan H.

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An investor has a total of $26,400 deposited in 3 different accounts, which earn annual interset rates of 6%, 5%, 4%. The amount deposited in the 6% account is twice the amount in the 5% account. If the 3 acccounts earn a total annual nterest of $1331. How much money is deposited in each account?
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Quantity Eq: x + y + z = 26400
Quantity Eq: x - 2y + 0 = 0
Interest Eq: 0.06 + 0.05y + 0.04z = 1331
----------------------------------------
solve the system by any means you know to get:
----------
x = 11000 (amt. invested at 6%)
y = 5500 (amt. invested at 5%)
z = 9900 (amt. invested at 4%)
===================================
Chers,
stan H.

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value of the house today is 500,000
in 5 years, the house will appreciate 5 years worth of interest which makes the formula for the future value of the house:
500,000 * (1.05)^5 = 638140.78
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if he invests in a project at the end of each year and the project earns 12% a year, then he would have to invest 100449.57 each year to equal 638140.78 at the end of the 5th year.
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this is how it works out:
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at the end of the first year he invests: $100,449.57
at the end of the second year this is multiplied by 1.12 to equal: $112,503.52
he invests an additional $100,449.57 to make this equal: $212,953.09
at the end of the third year this is multiplied by 1.12 to equal: $238,507.46
he invests an additional $100,449.57 to make this equal: $338,957.03
at the end of the fourth year this is multiplied by 1.12 to equal: $379,631.87
he invests an additional $100,449.57 to make this equal: $480,081.44
at the end of the fifth year this is multiplied by 1.12 to equal: $537,691.22
he invests an additional $100,449.57 to make this equal: $638,140.79
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he has invested 100,449.57 at the end of each year and this has accumulated and grown to equal $638,140.79 by the end of the fifth year.
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the value of the house has grown 5% per year for 5 years to equal $638,140.79.
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he has invested just enough money to buy the house with cash assuming no taxes have to be paid on the investment.
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there is a formula to derive this.
that formula has to do with the annuity from a future amount.
i used a calculator to get the answer.
if you had to use the formula, the formula would be:

which is the same as:

-----
FV is the future value which is the same as future amount.
i is the periodic interest rate which is annual in this case.
n is the number of time periods which is years in this case.
PMT is the annual payment.
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this formula is for a payment at the end of a period which was what your problem was asking about.
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i checked the formula out and it works.

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(3/4)/(a/b)=4/3
3/4=4a/3b
16a=9b
a=9
b=16
a*b=9*16=144 ans.

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.08x+.07(18,000-x)=1,370
.08x+1,260-.07x=1,370
.01x=1,370-1,260
.01x=110
x=110/.01
x=11,000 invested @ 8%.
18,000-11,000=7,000 invested @ 7%.
Proof:
.08*11,000+.07*7,000=1,370
880+490=1,370
1,370=1,370

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I am guessing that there must be some missing info (like maybe investing for more than a single year).
It "doesn't work" because given the numbers you have - "you can't get there from here".
Let's say the broker put the entire amount at 8% for a year. In that case, the interest is 13000*08 = 1040. Which is less than the value the problem stated was returned.
The math does not lie. The reason 46000>13000 is because the math, as provided, doesn't "work".
When you get an answer that doesn't make sense, like 5 = 7 or somesuch, then that means "you can't do whatever was being suggested could be done".
The fact that you were aware enough to realize that the answer is not 46000 and -33000 shows you are on the right track mathematically. Good for you!

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you must first figure the earnings per share which would be
:
earnings(1.5million)/number of shares(1 million
:
eps=$1.5 (earnings per share)
:
a PE(price per earnings) ratio is simply what your pay in multiples above what the earnings are.....if the earnings are 1.5 dollars per share a 15 PE or multiple would be 15 times that amount
:
therefore $ is the price that would be paid on Ted's stock if the equaled the industry PE multiple of 15.

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8x+9y=11
9y=-6x+11
y=-6x/9+11/9
y=-2x/3+11/9
Graphing this equation we get:
(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, -2x/3 +11/9).
(-6,8)
8*-6+9*8=11
-48+72=11
24=11
Thus (-6,8) are not valid answers to the x & y values in this equation.
Also the x & y values in the table don't fit this equation.
What problem are you trying to solve?????

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KIM SPENT TWO FIFTHS OF HER SALARY ON A SHIRT AND A HAT. THE SHIRT COST THREE TIMES AS MUCH AS THE HAT. IF SHE HAS $36.00 LEFT, HOW MUCH DID THE HAT COST?
----
Her salary = s + h + 36
----------------------------
s = 3h
s+h = (2/5)[s+h+36]
--------------------------
Substitute to solve for "h":
3h + h = (2/5)[3h + h + 36]
4h = (2/5)[4h + 36]
20h = 2[4h+36]
10h = 4h + 36
6h = 36
h = $6 (the hat cost)
============================
Cheers,
Stan H.

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Please solve the following question
10th root of 2.5/10
pls provide each steps clearly.
------------------
If you mean
Using a calculator, get
= 1.095958226...
Divide that by 10,
= 0.1095958226...
There aren't many steps.
------------
Using logs:
get the log of 2.5
log(2.5) = 0.397940008...
Divide that by 10
= 0.0397940008...
Get the antilog (raise 10 to that power)
10^0.0397940008 = 1.095958226...
Divide that by 10, same answer as above.
----------------
The number of steps depends on the number of buttons on your calculator.

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Your teacher is giving a test worth 150 points. There are 46 three and five point question on the test. How many of each question aron the test?
---------------
Quantity equation: T + F = 46
Point equation: 3T + 5F = 150
---------------------------------------
Multiply thru 1st equation by 3:
3T + 3F = 138
3T + 5F = 150
----------------------
Subtract 1st from 2nd and solve for "F":
2F = 12
F = 6 (# of five point questions)
--------------------------
Since T+F = 46, T= 40 (# of three point questions)
=======================
Cheers,
Stan H.

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a and b is positive integer.how could you get solution this equation?
3power a -7 power b=0
-----------------


a*log(3) = b*log(7)
a/b = log(7)/log(3) =~ 1.7712
---------------
It's difficult, and maybe impossible, to prove that there are no 2 integers with that ratio.
However, it is not possible to find a and b that satisfy the given conditions except a = b = 0.
3 to any integer power will have factors of only 3's, no 7's, and vice versa.

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3*(6+12/(4-2)) 3*(18/2)=3*9=27
Perform the function in the numerator and denominator and simplify.

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First thing. Please stop typing in all CAPS. It is the electronic equivalent of shouting, therefore both rude and annoying. Thank you.

As to your question:

You can't say anything about liquidity because you don't know the character of the current assets. Those assets may or may not be liquid. Hence, answers A and C can be excluded.

Since there is no information in the problem that would indicate whether or not the increase in current assets has any impact either way on profitability, you can also exclude answer D.

B is the only one that is left, and it makes sense because the investment in current assets has to come from somewhere, and that somewhere is Net Working Capital.

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the store offering the 30% discount has the better deal. why? there 30% is taken from a higher dollar amount whereas the other store does 20% on the original price and then 10% on that discounted price.
:
x-.3x=.7x(cost)
:
x-.2x=.8x-.1(.8x)=.72x(cost)

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Shakira is the manager of a 200-unit apartment complex. She is exploring how the monthly rent affects the number of vancant apartments in the complex. She found that she will rent all the apartments if she sets the monthly rent at $400, and found that for each $50 increase in the monthly rent, one additional apartment will remain vacant.
She is part owner of the apartment complex, she would like to set the rent so that she can actually make some money.
-----------------
Revenue = price per apartment * # of apartments rented
R = (400+50x)(200-x) = 80000 + 800x - 50x
--------------------------------------
1. How many apartments should remain vacant so that the monthly rental revenue will be as large as possible.
max occurs when x = -b/2a = -800/(2*-50) = 8 (# of vacant apartments)
--------------------------------------

2. What monthly rent should she charge for each apartment in the apartment complex.
R(8) = (400+50*8)(200-8) = $153,600
--------------------------------------
3. draw a graph between monthly rent and number of occupied apartments. Write the equation of the graph.
(occupied , rent): (200,400), (199,450)
slope = (450-400)/(199-200) = -50
intercept: 400 = -50*200 + b
b = 10400
EQUATION:
rent = -50*occupied + b
r(x) = -50x + 10400

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4. Use formula to find the vertex of the equation.
Vertex: Which equation ?
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Cheers,
Stan H.

You can put this solution on YOUR website!
if a salesman made 25,000.00 in sales after 3 months, and after 23 months he made 68,000.00, how much would he make after 32 months? I can't find a formula anywhere.
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You have two points; generate an equation to find income:
Points: (3,25000.00) and (23,68000..00)
slope = (68000-25000)/(23-3) = (43,000/20) = 2150
intercept: 25000= 2150*3 + b
b = 18550
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Equation:
income = 2150(months) + 18550
income(23) = 2150*23 + 18550
income(23) = 68,000
Cheers,
Stan H.