Question

How is an annuity due similar to an ordinary annuity (how is it different)? Explain why an n-period annuity due is exactly the same as an “(n-1) period ordinary annuity plus an extra payment at time zero. Given this, explain how you could compute the PV of an n-period annuity due using the normal = ordinary annuity settings of a financial calculator. Note: This idea is really getting at the fundamental concept of viewing cash flow streams as represented in a time line and solving that time line and not “memorizing” specific cases, such as an annuity due case. Given this, one can solve most annuity due situations by drawing the time line and simply making adjustments and using the ordinary annuity functions.

Answer 1

In an ordinary annuity the cash flows are realized at the end of the period while in an annuity due the cash flows are paid at the beginning. In an n-1 ordinary annuity there are n-1 cash flows at the end of the period. On the other hand in an n annuity due there are n-1 cash flows at the beginning plus an additional cash flow at the upfront period. So this additional cash flow must be added to the n-1 ordinary annuity to make them equivalent.

So to get the value of n period annuity due we can just calculate the value of ordinary annuity and multiply by a factor of (1+r) where r is the interest rate. This is because since the cash flows in the annuity due is realized one period earlier, there is one period less to discount for each cash flow while arriving at the present value