Professor jt receives a perpetuity for his retirement that pays $300 at the end of year 6, $600 at the end of year 10, $900 at the end of year 14, with payments continuing to be made every four years thereafter at an amount equal to $300 more than the immediately preceding payment. the present value of the third payment is $535.35. calculate the present value of this perpetuity.

PV at time zero=$12621.48

Step-by-step explanation:

Looking at the given data we can see that perpetuity is increasing arithmetically with payment after ever 4 years

Starting payment is $300 at time 6

payment reaches to $900 at time 14

Present value of the 3rd payment = $535.35

Note:

Considering the 4 year interval starting time will be at 2 which is half i.e 0.5 of 4 year that is why we are going to use 3.5 years for any time and 0.5 years for time zero

Present value of time 14 at $900 is discounted back to $535.35 for 3.5 years period

PV=P/(1+i)^n

where:

P is the given value at the time

n is the number of years

i is the interest rate

PV is the present value in given time

Solving above equation for time 4:

535.35*(1+i)^3.5=900

i=0.1599≅0.16

So interest i is 16%

Perpetuity immediate at present time:

P/i +Q/i^2

where:

P is $300 which is amount of first period

Q is $300 which is the increment after each interval

300/0.16 +300/0.16^2 =13593.75

The above value is discount for 2 years not for 4 years

So in order to find present value at time zero we must discount it back

Now:

PV=P/(1+i)^n

where:

P is the given value at the time

n is the number of years

i is the interest rate

PV is the present value in given time

PV=$13593.75/(1=0.16)^0.5

PV at time zero=$12621.48

up

step-by-step explanation:

the orientation of the parabolas can easily be found by analysing the power of x and y and their signs. if x is squared , parabola opens up and also if its coefficient is negative it opens down. if y is squared , the parabola opens right and also if its coefficient is negative it opens left. however in order to do the above analysis our equation must be in standard form .

our parabola is

which is not standard form of any parabola . hence we square on both hand side and convert it into standard form.

hence we see that x is squared and its coefficient is non negative . there for it opens up.

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step-by-step explanation:

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