# Value of annual perpetuity?

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This topic contains 4 replies, has 4 voices, and was last updated by  croki11 2 years, 9 months ago.

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• Sangria9
Moderator

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?

Sangria9
Moderator

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

arslan9898
Participant

means

5000/0.08 =400

and

400/0.08 = 370

Ken
Participant

@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..

croki11
Participant

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

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