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Perpetuity practice question

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  • Perpetuity practice question

    Hi there,

    A 30-year annuity-immediate with 2,000 payable at the end of every 6 months and a 30-year annuity-immediate with 10,000 payable at the end of every 6 years are to be replaced by a perpetuity paying R every 3 months. You are given that i(4) = .08. Find R.

    I assume j is the 6 month rate= (1.02)^2-1
    So first annuity has PV=2000*a angle 60 j=44906.33

    The second annuity... I assume h is the 6 year rate=(1.02)^24-1
    So this one has present value=10.000*a angle 5 yrs h=14908,81

    I add these 2=59815.14

    The perpetuity's interest rate =(1.02)^4-1
    The perpetuity's PV=R*1/(i. a angle)=12.13
    But R should be found as 1196.33

    Where do I make the mistake?

  • #2
    The annuity formulas and answer are correct. However, the perpetuity's interest rate is 2%, since it is payable every 3 months. And the PV of a perpetuity is just R/i, so

    59815 = R/.02, which you get 1196.33


    • #3
      Thank you for the explanation Killjacker.