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The present value of the basic annuity-immediate lasting n interest periods is used frequently. If the accumulation function to be used is clear, the present value is de noted by the annuity symbol an. If a compound interest accumulation function is operative, and the effective interest rate for the payment period is i, then you often write ani instead of just am. This allows you to emphasize the effective interest rate used. The annuity symbol a nll is read "a angle n at interest rate i Equation (3.2.3) may now be rewritten (3.2.4) 1-v can be rewritten as the present value relation 1 The identity am iami l v"; a unit invested for n years will produce end-of-year interest o i for each of the n years, as well as the return of the unit investment at the end of the n years. IMPORTANT FACT 3.2.5 With an annuity-immediate, you must wait one period to start receiv ing payments. The present value of a basic annuity-immediate lasting n periods is denoted by an. It gives the value of the annuity one period before the first payment. It is also useful to have a symbol giving the accumulated value of a basic annuity immediate lasting n periods at the time of its final payment. The annuity sym- bol sn or sni denotes this accumulated value Of course the latter is only used when the accumulation is governed by the compound interest accumulation function a(t) (1 i) Read the symbol smi as "s angle n at interest rate i

Explanation / Answer

For i=0, there is no need to use this formula because if interest rate is 0 we can directly calculate annuity by dividing amount by years in how many years we have to pay amount.

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