Question

Ordinary Annuities and Annuities Due As discussed in the text, an annuity due is identical to an ordinary annuity except that the periodic payments occur at the beginning of each period and not at the end of the period. Show that the relationship between the value of an ordinary annuity and the value of an otherwise equivalent annuity due is: Annuity due value = Ordinary annuity value × (1 + r ) Show this for both present and future values.

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Answer 1

To solve for the PVA due:

PVA = C/(1 +r)¹ +C/(1 +r)² + …. +C/(1 +r)^t

PVA due= C + C/(1 +r)¹ +C/(1 +r)² + …. +C/(1 +r)^t –1

PVA due= (1 +r)[ C/(1 +r)¹ +C/(1 +r)² + …. +C/(1 +r)^t]

PVA due = (1 +r) PVA

And the FVA due is:

FVA =C + C(1 +r) +C(1 +r)2 + …. +C(1 +r)t –1FVA due =C(1 +r) + C(1 +r)2 + …. +C(1 +r)tFVA due = (1 +r)[C + C(1 +r) + …. +C(1 +r)t–1]FVA due = (1 +r)FVA