Final answer:
The expression in brackets in the future value of an annuity formula relates to the sum of a geometric series representing the future value of payments over a number of periods. It can't be directly identified as any of the provided options but is most closely associated with the number of periods and the compound interest calculated over these periods.
Step-by-step explanation:
In the formula for the future value of an annuity, the expression in brackets, which typically represents the sum of the geometric series that arises from the annuity payments, is equal to the future sum of the payments considering the effect of interest rates over the number of periods. It is not the interest rate itself, nor the present value or the payment amount directly. Instead, it's used to calculate the total future value received from the annuity after n periods at interest rate i. The correct answer is not explicitly stated among the options a) Interest rate b) Present value c) Payment amount d) Number of periods, but it is most closely related to the number of periods as it's a factor in the growth due to compounding.
When we use the formula for calculating the future value (FV) of an annuity in the case of compound interest, the formula is generally expressed as:
FV = P × (1 + r)^t
Where 'P' is the principal amount, 'r' is the interest rate per period, and 't' is the number of periods the money is invested or borrowed for. Compound interest is the interest calculation on the principal plus the accumulated interest over the number of periods.