Questions on Algebra in Finance answered by real tutors!

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There isn't enough information to know what
year it's starting at.
I'm assuming that is the number of years
that have passed, and is the 1st year



million acres the 1st year
When does the land total million acres?


Subtract from both sides

Take the log to the base of both sides, noting that








and

is about equal to 36 years and 5 months.
Sometime in the 5th month of the 36th year,
the farm acres drops below

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you're using the wrong formula.

here's a list of the formulas you should use for the type of problems you will encounter mostly.

LIST OF FINANCIAL FORMULAS

The particular formula you are interested in is:

PAYMENT FOR A FUTURE VALUE

PMT = Payment per time period
FV = Future Value
i = Interest Rate per Time Period
n = Number of Time Periods

You do, however, have to make an adjustment.

You start off with $2400 and you want to end up with $4800.

The formula assumes the starting value is $0.

You need to subtract $2400 from the $4800 so that your starting value is $0 and your ending value is $2400.

You can then substitute in the formula as follows:



where:

FV = future value = $2400
i = .08/12 = .0066666667
n = 2*12 = 24

Now you can use the formula as follows:




This becomes



which becomes:



which becomes:



The future value of your payments will be $2400.

Add this to the $2400 that you started with and you will have $4800.

Because you were compounding monthly, your annual interest of 8% needed to be divided by 12 and converted to a straight rate before plugging into the formula.

8% / 12% = .666666667% / 100% = .0066666667.

Your number of years needed to be multiplied by 12 in order to get number of months because your payments were on a monthly basic and your compounding of interest was on a monthly basis.

That's why we multiplied 2 years by 12 to get 24 months.

Once everything was in sync, you could use the formula.

The formula you were using was not a payment formula.

It was a future value of a present amount formula.

You could not solve for payments using that formula.

you can confirm your answer is correct by plugging the value of the payment back into the original formula.

I used a financial calculator which is the easiest way if you know how to use it.

You can also used financial formulas in EXCEL if you know how to use them and you have a copy of EXCEL on your computer.

There are also financial calculators on the web that you can use to check your work if you know how to use them.

If you are interested in one, let me know and I'll scour the web for you.

They can help, but you do have to know how to use them based on the problems you have to solve.

Example is your problem. If you didn't know that you had to subtract the present value to use the formula, you never would find the correct answer.

I MADE A MISTAKE.

I assumed the $2400 was NOT earning any money.

That changes the problem.

Big time.

Since the $2400 is invested also, then the problem changes as follows:

You first calculate the future value of the $2400 already invested in the account.

That comes out to be (using your original formula)

FV(PA) = $2400 * (1.006666667)^24 = $2814.931036

That's what $2400 earns in 2 years compounded monthly.

THAT's the amount you have to subtract from your $4800.

The result of that subtraction is what you need to make by plugging it into the payment for a future value formula.

$4800 - 2814.931036 = 1985.068964.

The payment formula becomes:



PMT(FV) now comes out to be:

PMT(FV) = $76.54549949

You have $2400 in the account that earns you $2814.931036 by the end of 2 years.

You have payments of $76.54549949 per month that earn you $1985.068964 by the end of 2 years.

You add up $2814... and $1985... and you have $4800 at the end of 2 years.

To show you how this actually works in the account, I'm going to cut the number of months down to 5 because 24 months is too many months to show in such detail.

The future worth of $2400 at .0066666667 interest per month for 5 months is equal to $2481.073802
The future worth of $76.54549949 payments for 5 months is equal to $387.8646645

Total future worth is $387.8646645 + $2481.073802 = $2868.938467

This is the money you will have in the account after 5 months.

Here's how it works:

all numbers truncated on display but full numbers used for calculations.

At end of month 1 you will have $2400 * 1.0067 + $76 = $2492.5
At end of month 2 you will have $2492.5 * 1.0067 + $76 = $2585.7
At end of month 3 you will have $2585.7 * 1.0067 + 76 = $2679.4
At end of month 4 you will have $2679.4 * 1.0067 + 76 = $2773.9
At end of month 5 you will have $2773.9 * 1.0067 + 76 = $2868.938466

The number calculated in detail after 5 months is the same number we calculated using the future value of present value formula and the payment for a future value formujla.

The same process applies to your problem except you carry it out 24 months instead of 5.

Sorry for the mistake but it was instructive so I left it in. The mistake I made would be a common mistake if you didn't know better. I should have.

You needed to break your problem into two parts.

The first part was the initial investment where you used the formula you started with.

You used this to calculate what the initial investment would be worth at the end of the 2 years.

You then subtracted that amount from $4800 so you could calculate how much payments you needed to make each month to come up with the difference.

At the end, the sum of the future value of your initial investment plus the sum of the future value of the payments needed to be equal to $4800.

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how many years it will take for the two accounts to reach the same balance. 1000 investment with a rate of 5.25% compounded continuously and 800 investment with a rate of 6.25% compounded continously. i got this far
1000e^.0525=800e^.0625
----------------------
1000e^.0525t=800e^.0625t You need the time in the exponents
--------------
Take the ln of both sides
ln(1000) + 0.0525t = ln(800) + 0.0625t
0.0625t - 0.0525t = ln(1000) - ln(800)
0.01t =~ 0.223144
t =~ 22.3144 years (assuming the int rates are annual)

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Assume it should read:
A 67,500 estate is to be split among four children and a grandchild.
Each child gets the same amount, and the grandchild gets half the amount.
How much will each receive?
:
Let x = amt received by the grandchild
then
2x = amt received by the children
:
x + 4(2x) = 67500
x + 8x = 67500
9x = 67500
x =
x = $7500 received by the grandchild
then
2(7500) = $15000 received the the children
:
:
Check 4(15000) + 7500 = 67500

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.06X+.04(14,000-X)=720
.06X+560-.04X=720
.02X=720-560
.02X=160
X=160/.02
X=8,000 AMOUNT INVESTED @ 6%.
14,000-8,000=6,000 AMOUNT INVESTED @ 4%
PROOF:
.06*8,000+.04*6,000=720
480+240=720
720=720

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D+N=81 OR D=81-N
.10D+.05N=5.80
.10(81-N)+.05N=5.80
8.10-.10N+.05N=5.80
-.05N=5.80-8.10
-.05N=-2.30
N=-2.30/-.05
N=46 NICKELS.
D=81-46=35 DIMES.
PROOF:
.10*35+.05*46=5.80
3.50+2.30=5.80
5.80=5.80

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350 * (1.06)^t = future value of this account.

at the end of 1 year, the account will have 350 * (1.06)^1 = 371

at the end of 2 years, the account will have 350 * (1.06)2 = 393.26

that comes out as 350 * 1.06 * 1.06

since 350 * 1.06 = 371 * 1.06 = 393.26, the interest earned each year is combined with the principal and then interest is earned on the sum.

at the end of 10 years, the account will have 350 * (1.06)^10 = 626.80

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let x=sunflower, so 3x=raisins

(4)(x) + (1.5)(3x) = 34

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First line is y = .15x + .79
Second line is 0.11x-y= -0.85
Solve for y in the second line to get:
y = .11x + .85
These lines are not parallel or perpendicular because the slopes are not the same or negative reciprocals of each other.

The slope-intercept form of a straight line is y = mx + b where m is the slope.
First line has slope of .15
Second line has slope of .11

These lines will intersect.
Solve these 2 equations simultaneously to find the intersection.

The equations are:
y = .15x + .79
y = .11x + .85

Mulltiply first eqution by 11 and second equation by 15 to get:

11y = 1.65x + 8.69
15y = 1.65x + 12.75

subtract second equation from first to get:

4y = 4.06

divide both sides by 4 to get:

y = 1.015

substitute in first equation original to get:

1.015 = .15x + .79

solve for x to get:

.15x = 1.015 - .79 = .225 which makes x = .225/.15 = 1.5

y = 1.015 and x = 1.5

substitute in second original equation to get:

1.015 = .11x + .85 becomes 1.015 = .11*1.5 + .85 = .165 + .85 = 1.015 which is true.

The two lines intersect at (x,y) = (1.5,1.015)

graph of these two equations is:



horizontal line was put in at y = 1.015 to help you see the intersection point better.

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the formula for interest is I=P x R x T
so you times p and r then it is the answer and t u divide the answer u got from p and r u divide it in to I so it I divided by the answer from p and r then you get T=time

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Hello,
A little more information is needed but let me see if I can help you out.
If the 8% is a simple interest then we can multiply 8% times $200.
.08($200)= $16 interest for one year.The second year multiply 8% times $216
.08(216)=$17.28 Add this to $216 for a total of $233.28
Now for the 3rd year multiply 8% times 233.38
.08(233.38)=$18.66 interest added to $233.38 for a total of $252.04
There is a faster way but I wanted to show you how it works so you have a better understanding of how it works.
RJ Toftness
www.math-unlock.com

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Let represent the amount invested at 8.5%. Then the amount invested at 6% would be .

The amount of interest earned on the 8.5% money is then and the amount of interest earned on the 6% money is and these two amounts must add up to $5000.



Solve for to get the 8.5% amount. Subtract that from 70000 to get the 6% amount.

John

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Start with the compound interest formula


Plug in p=5000, r=0.03 (this is the decimal form of 3% interest), n=12, and t=7


Divide 0.03 by 12 to get 0.0025


Multiply the exponents 12 and 7 to get 84


Add 1 and 0.0025 to get 1.0025


Raise 1.0025 to the 84 th power to get 1.23335480054924


Multiply 5000 and 1.23335480054924 to get 6166.77400274618


So if you invest $5,000 at an interest rate of 3%, which is compounded 12 times a year for 7 years, the return is about $6,166.77 (which is rounded to the nearest cent)

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5)
P=A/(1+r/n)^nt
P=15000/(1.09)^8
P=15000/(1.992562642)
P=$7528
-----------------------
P=15000/(1.09)^6
P=15000/1.6771
P=$8940
-----------------------
13)
FV=P(1+r)^9
FV=7455(1.09)^9
FV=7455*2.171893279
FV=$16191
-----------------------
6)
FV=(P((1+i)^n-1)/i
FV=(5000((1.1)^6-1)/.1
FV=(5000((1.771561)-1)/.1
FV=3857.81/.1
FV=$38578.05
---------------

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2.) Determine the future values if $5,000 is invested in each of the following situations:
a.) 5 percent for ten years
Begin with $100 - - - > 5 percent for 1 year - - > 105
then with each $1 - - - > 105/100 = 1.05 after 1 year
Then for $5,000 it would be 5,000 * 1.05 after 1 year
and then 5,000 * 1.05 * 1.05 after 2 year
for 10 year investment
it would be 5,000 * (1.05)^10 = $8144.473 Ans

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68=104 base 8

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21.69/.73=$29.71

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.12x+.06(240-x)=.09*240
.12x+14.4-.06x=21.6
.06x=21.6-14.4
.06x=7.2
x=7.2/.06
x=120 pounds of soybeans is used.
240-120=120 pounds of cornmeal is used.
Proof:
.12*120+.06*120=.09*240
14.4+7.2=21.6
21.6=21.6

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in 1995 the life span of males in a certain country was 64.7 years. in 2001 it was 66.7 years. Let E represent the life span in year t represent the number of years since 1995.
:
Find the slope
In 1995; x1=0 and y1=64.7
In 2001; x2=6 and y2=66.7
:
Find the slope (m) using the slope equation: m =
m = = =
therefore:
The Linear function E(t) that fits the data is.
E(t)= t + 64.7
:
E(11)= (11) + 64.7
E(11)= 3.67 + 64.7
E(11)= 68.4 yrs is the life expectancy in 2006

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Calculate:



Hmmm...maybe she has blue eyes.

John

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The perimeter of a rectangle is given by:



but we want to fix the width at 10 and hold the perimeter greater than 82, so:



Solve for :





John

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Let represent the number of dimes. Then the number of quarters must be

Since each dime is worth 10 cents, the value of the dimes, in cents is: . Likewise, the value of the quarters, each worth 25 cents, must be

The value of the dimes plus the value of the quarters must equal the total value of all the coins, which is given as $5.05, but which can be expressed as 505 cents. So:



Just solve for to get the number of dimes, double that and add one to get the number of quarters.

John

solver91311 showed you how to do it the way you were
trying it. You can indeed get the answer the way you're 
trying and the way solver91311 showed you, if you don't 
make a mistake.  But you aren't supposed to do it that
way!  Here's the way you're supposed to do it:



Write  as 



Consider  as 



Remove the parentheses by multiplying
the two inner exponents by the outer exponent:



Do the actual multiplying:



Since , replace  by 



But that is not scientific notation because
 is greater than , and the first part
of scientific notation must be between  and , inclusive
of 1 but exclusive of .  So write  in scientific
notation as :



Add the exponents of 10



Do the actual addition:



Edwin