Melody

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?

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

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

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.  :)

(-2-sqrt3) (-2+sqrt3)

What is your problem with this question?

Just expand it like this 

\(-2(-2+\sqrt3)\;\;\     -\sqrt3(-2+\sqrt3)\)

Post your answer or just the next step if you want and I will tell you if it is correct.  :)

What is the common ratio of the geometric sequence? −23,−2,−6,−18,...,?

I believe this is supoposed to be  −2/3,−2,−6,−18,...,?

The common ratio is given by     \(\frac{t_n}{t_{n-1}} \)

\(r=\frac{-2}{-2/3}=\frac{-6}{-2}=\frac{-18}{-6}=3\)

Centre (2,3) radius3

(X-2)^2+(y-3)^2=9

Who wants to know??

You are correct guest - I made a slight error, it should be 

+tan(pi/4)

and the final answer is +2

y= (sin(7pi)/6+tan(5pi/4))/cos(5pi/3)

Hi Max,

I think one of your brackets was in the wrong place ://

Otherwise yours was a great answer.  

\(y=\frac{ \frac{sin(7\pi)}{6}+tan(\frac{5\pi}{4})}{cos(\frac{5\pi}{3})}\\ y=\left( \frac{sin(7\pi)}{6}+tan(\frac{5\pi}{4})\right)\div cos(\frac{5\pi}{3})\\ y=\left( \frac{sin(\pi)}{6}-tan(\frac{\pi}{4})\right)\div cos(\frac{\pi}{3})\\ y=\left( 0-1\right)\div cos(\frac{\pi}{3})\\ y=-1\div \frac{1}{2}\\ =-2 \)