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Compound increasing annuity question

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  • Compound increasing annuity question

    There are some exam questions with compound increasing annuity using the formula:

    PVF=1/(1+e) [ (1-(1+j)^-n) / j] , where j = (i-e)/(1+e), where 'e' is the percentage increase of payment each year.

    I noticed some similar exam questions are answered using the geometric series formula to solve for the increasing values:

    a[1+r+r^2+....+r^(n-1)] = a[ (1-r^n)/(1-r)]

    I am confused at situations that use one formula versus the other. Can someone help explain what's the difference in using the two formulas and in what situations should each one be used.

    Thanks a lot!

  • #2
    The formulas are similar; however, the first is based upon the second. The second is the formula for the present value of an annuity-immediate (ordinary annuity) with level payments. The r in this situation is the discount factor (1/(1+i)).

    The first formula gives the present value of an annuity with payments which vary geometrically. If the first payment is one, and is made at the end of period 1, and then increases (or decreases, if negative) at a rate of k, and the interest rate is i. Then v=1/(1+i)
    present value = v + (1+k)v^2 + (1+k)^2*v^3 + ... + (1+k)^(n-1)*v^n
    =[1-((1+k)v)^n]/(i-k)

    Does this help at all?

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