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  • annuity immediate

    Hi there,

    I have to find an expression for the present value of an annuity immediate with a period of 2n years that pays 1,2,3,4, ... , n,n,n,n, ... ,n

    The nominal rate of interest is i^12 = .06

    I was thinking that we could break up the problem into 2 sections, the first n years, and then the second n years, becuase the first n years the payments are an arithmetically increasing payment annutiy where the payments go 1,2,3,...,n and then the next n years each payment is just n like a regular annuity.

    From Kellisons theory of interest page 110, he gives a formula which I think would work for the first part:

    A = Pa(n,j) + Q[a(n,j)-nv^n]/i where P is the first payment and Q is how much it increases by, which would both be 1 in this problem, so then it would look like A = a(n,j) + [a(n,j)-nv^n]/i

    and then the second part would just be a regular annuity with n*a(n,j)

    where a(n,j) is annuity immediate with interest rate j = annual effective rate converted from i^12

    I mean this seems easy enough, but something just does not seem right. The second part should relate to the first part somehow.

    Any help with this is much appreciated!

    thanks in advance
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