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Come on Kcc - We are not here to do all your homework for you!

A page of Latex explanation contributed by MaxWong.  Thanks Max    

Thanks Max,

I will add this to our LaTex thread that is kept with the sticky topics.

This thread is in a bit of a mess I am afraid but I still find it useful occasionally.

If you want to voluteer to do a new cleaned up version that would be really good.

(You would just need to include the address of the original one so we don't lose it)

If you don't want to or do not have time that is fine.  :)

Also,

If you are usually able to edit your posts you are really lucky.  Most of us, including me, are never able to do that any more.  We used to be able to but it has not worked for a long time now.  That is one of the reasons that things are no longer well organised.  Many threads really need the editing ability to keep them tidy. :(

That is ok guest :)

The last bit is not really a part of the question.

The question is to find the present value which is e117,965

I just continued on for Max's benefit  - I wanted to help him to understand what the question was about :)

Maybe it helped the poster,  Kcc2468 better understand as well :)

Are you sure that you understand?

SORRY MELODY: DIDN'T READ THE LAST BIT OF YOUR CALCULATION, WHICH IS PERFECTLY CORRECT. SORRY ABOUT THAT!.

2. A factory has fixed monthly costs of e20,000.  [ I am assuming that is 20000 per month]

The material costs per unit is e2.5 and the sale price is e 6 per unit.

(a) Find the total cost function,    TC=20000+2.5U

and the total revenue function.     TR=6U  

(I am using U for units - I am nor sure if there is aome other letter that should be used)

(b) How many units need to be sold per month to break even?

20000+2.5U=6U

20000          = 3.5U

20000/3.5    =U

U = 5714   to the nearest unit

(c) Find the profit function, and determine the revenue when 10,000 units are sold per month.

P = revenue - cost

P = 6U-(20000+2.5U)

P = 3.5U - 20000

TR=6U

TR(10000)=6*10000 = e60000

(d) How many units need to be sold per month to yield a monthly profit of e 50,000?

P = 3.5U - 20000

3.5U - 20000>50000

3.5U>70000

U>70000/3.5

U>20,000

20,000 units will need to be sold in the month

Melody: You got everything right, except if the 500e were deposited in the the Bank @ 2% each and every month for 25 years, that would give you the FV of the annuity, which would amount to $194,410.56e.

Max you have found the amount that  500 will grow to in 25 years but this is not the question.

This is like a pension where e500 is paid every month for 25 years.

The question is asking - what would be an equivalent value to have in your hand now if the money is values at 2% pa.

This is the present value of an ordinary anuity

C=500,       i=0.02/12        n=25*12=300       PV unknown

500*((1-(1+0.02/12)^-300)/(0.02/12)) = 117965.0541267359729345119082314998414034840152410787338337814191407       

So the present value of this anuity is   e117,965.05

This means that if you were given e117,965 and put it in the bank at 2%/pa compounded monthly.

or

if you were given e500 every month for 25 years and you put each instalment in the back and it attracted 2%pa compounded monthly interest.  And you left all these instalments in the bank 

THEN

at the end of the 25 years both these scenarios will grow to exactly the same amount of money, namely

117965.05*(1+0.02/12)^300 = e194 410.56

(a) - They must deposit $309.17 every month for 10 years to have $40,000. Work this out and see if you can get the same amount.

(b) - Their monthly payment would be $889.33. The Bank should earn a total of $106,800.10 in interest over 25 years. Also, try to verify these numbers on your own and see if you can get the same numbers. If you have any problems, let us know.

Hi Kcc,

3. A couple save for a deposit and then take out a mortgage to buy a house as follows:

(a) They pay equal monthly amounts into a savings account which pays interest of 1.5% p.a. compounded monthly. What is the monthly amount they must deposit in order to have e 40,000 at the end of 10 years?

This is the furture value of an ordinary annuity problem.

i=0.015/12       C=unknown    n=120        FV=40000    

You can work this out yourself.   :)

(b) After ten years they buy a house for e200,000 using the e40,000 saved as a deposit. They take out a 25 year mortgage at the fixed rate of 4.5% p.a. compounded monthly. Compute the amount of the monthly repayment of the mortgage?

PV=160000   i=0.045/12        n=25*12       C= ?

Use PV of an ordinary anuity to work this bit out.

(c) How much does the bank earn on the mortgage?

you can do this bit I expect.  :)

what is the blanks in 4,9,..,25,36,.. please tell me thank you

4, 9, 16, 25, 36, 49, 64, 81.........etc. Add the odd numbers , 5, 7, 9, 11, 13, 15......etc to each term.

1(a) $500 x (1+2%)^{25 x 12}

    = $500 x 1.0230

    = $905.6807920516769 

    \(\approx\)$ 905.68

This is a trig question.

And there's one information missing. What's the actual distance (not the horizontal distance) from the hoop to the free-throw line?

This isn't a question.

1(a) $500 x (1+2%)^{25 x 12}

    = $500 x 1.02³⁰

     = $905.6807920516769 

    \(\approx\) $ 905.68

(b)(i)\(\quad(\frac{1+0.0339}{1})^1-1\\ = 0.0339\)

APR = 3.39%

(b)(ii) \(\quad (\frac{2+0.0329}{2})^2-1\\ = 0.033170602.....\)

APR = 3.32.....%

(b)(iii) \(\quad (\frac{4+0.0335}{4})^4-1\\ = 0.033923......\)

APR = 3.392.....%

(b)(iv) \(\quad (\frac{12+0.034}{12})^{12}-1\\=0.0345348......\)

APR = 3.45......%

Which of these gives the cheapest option when taking out a loan for two years?

3.29% p.a. compounded semi-annually.

How much interest would it cost to borrow $1,000 for two years under the cheapest option?

1000 x 3.32% x 2

= $66.4

(c) 1000 x (1+2.5%)^{4 x 10}

= 1000 x 2.685063838

= $2685.1 approx.

(d) f(x) = 2 - 3ln(x) + 3x

\(f'(x)= \frac{3}{x}+3\\ f'(1)= \frac{3}{1}+3 = 6\)

f(x) = 2x²e^x

\(f'(x)= 2xe^x(x+2)\\ f'(1)= 2(1)(e)(1+2)= 6e\)

g(x) = 1 + x²

\(g'(x)= 2x\\ g'(1)= 2(1)=2\)

(e) \(f(x)=x^3-2x^2-4x\\ f'(x)= 3x^2-4x-4\\ f''(x)= 6x-4\)

I don't know what's critical point and local maximum.......

......and don't forget Leap Years have an extra day......in 10 years you could have at LEAST two leap yeas and possibly THREE

Why can't I edit my answer again..... Never mind.

If you want to type a degree sign do {something}^{\circ}

Example: \(180^{\circ}\) Latex code: 180^{\circ}

\(Interior \space angle \space sum \space of \space a\space 9\space sided \space polygon\\={(9-2)\times180^{\circ}}\\=1260^{\circ}\)

It is a kind of machine that follows the 'IPO'.

Input : You input an equation in the calc.

Process: The calc. help you calculate.

Output: The result is the output of the calc.

And this could be done within a second.

Then join the forum! :D 

E.g.

1) \(\frac{7}{21}=\frac{7\div7}{21\div7}=\frac{1}{3}\)

2)\(\frac{108}{216}=\frac{108\div108}{216\div108}=\frac{1}{2}\)

3)\(\frac{45}{150}=\frac{45\div15}{150\div15}=\frac{3}{10}\)

\(-\frac{2}{3}\times \frac{1}{3}=-\frac{2}{9}\)

LaTeX code: -\frac{2}{3}\times \frac{1}{3} = -\frac{2}{9}

\(y=\frac{1}{2}x+1\\ y= -3x+8\)_------(2)^------(1)

(1)-(2): 0 = \(\frac{7}{2}x-7\)

        \(\frac{7}{2}x=7\\x=2\)

\(y = (\frac{1}{2})(2)+1\\y=1+1\\y=2\)

If it's a maths question, it's 19

If it's a joke, it's 21

and I don't know why 9+10=21 is a joke.