Value of annual perpetuity? — OpenTuition Forums

SSangria914y ago

Please help with this question:
Mr Manaton has recentrly won a competition where he has the choice between receiving $5,000 now or an annual amount forever starting now (a level perpetuity starting immediately). The interest rate is 8% per annum.
What would be the value of the annual perpetuity to the nearest $?
A. $370
B. $500
C. $400
D. $620

Why the answer is A?

SSangria914y ago#1

Yes, pleeeease explain! :)
I don't understand this example...
And I don't understand your math: 5000 / 8% = 62 500 and 400 / 8% = 5000

Aarslan989814y ago#2

means

5000/0.08 =400

and

400/0.08 = 370

((deleted)14y ago#3

@sangria9 said:
Yes, pleeeease explain! :)
I don't understand this example...
And I don't understand your math: 5000 / 8% = 62 500 and 400 / 8% = 5000

ok
Present value of a perpetuty formula is :
PV= cashflow / rate of interest
PV= cash flow * 1/rate of interest so..1/rate is perp... factor
Assumption: This is the prep... starting in 1 year time..
As per your question it is starting now! so we add one factor year to this..
now ..
Step 1: 1/.08=12.5
Step 2: Add 1 ....12.5+1=13.5
Step 3: cal......5000/13.5=370 approx

Here PV is given as 5000..so we rearrange the formula...to PV/Factor as we are looking for a cash flow..

Ccroki1114y ago#4

Hi,
Great answer I am learning as well with this explanation:-) Thanks

RRuksana9y ago#5

We assume the PV to be an "a" The general formula for annual perpetuity is PV x (1 + 1/rate of interest)= Annual Perpetuity a x (1+1/ 0.08)= 5000 a x ( 1.08/0.08)=5000 a x (13.5)= 5000 a=5000/13.5 a= 370.37 or 370 to the nearest $

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