Final answer:
The change in the index over the period of an annuity is influenced by inflation and interest rates. Inflation rates are derived from index numbers representing the cost of goods, while changes in interest rates affect the present value of future dollar payments and the investment's value.
Step-by-step explanation:
The change in the index over the period of an annuity is determined by various factors including inflation rates and interest rates.
Inflation rates can be calculated using index numbers that are proportionate to the total dollar cost of purchasing a basket of goods.
Using the percentage change formula, one can determine the inflation rate from one period to the next, such as from period 1 to period 2.
If we take the example provided where the index number changes from 93.4 to 99.5, the inflation rate would be calculated as (99.5 - 93.4) / 93.4 = 0.065, which equates to a 6.5% inflation rate.
On the other hand, interest rates also affect the present value of an annuity.
If, for instance, the interest rate rises from 8% to 11%, the actual dollar payments remain the same; however, their present value decreases because they are now discounted at a higher rate. Thus, the investment's value falls despite the nominal dollar payments staying the same, affecting the underlying index over the annuity period.