Value of annual perpetuity?

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  • Profile photo of Sangria9
    Sangria9
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    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?


    Profile photo of Sangria9
    Sangria9
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    Yes, pleeeease explain! :)
    I don’t understand this example…
    And I don’t understand your math: 5000 / 8% = 62 500 and 400 / 8% = 5000


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    arslan9898
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    means

    5000/0.08 =400

    and

    400/0.08 = 370


    Profile photo of Ken
    Ken
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    @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..


    Profile photo of croki11
    croki11
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    Hi,
    Great answer I am learning as well with this explanation:-) Thanks

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