University:
Grand Rapids Community College
Course:
Financial and Managerial Accounting: Information for Decisions - John J. Wild
Academic year:

2024
Views:

39

Pages:

2
Author:

stud_ice13

The future value (FV) of an annuity represents the total accumulated amount of a series of equal periodic payments, compounded with interest up to a specific date. This calculation helps estimate the final value of consistent investments or savings over time, factoring in interest. Key Concepts 1. Future Value of an Annuity Formula: To calculate the FV of an ordinary annuity (with payments at the end of each period), we apply the formula: FV=PMT×(1+i)n−1iFV = PMT where: o o o PMT = payment amount per period i = interest rate per period n = number of payments This formula compiles each payment’s compounded value as of the last payment date, accounting for the accumulated interest on each periodic payment. 2. Using Future Value of Annuity Tables: A future value of an annuity table (e.g., Table B.4) provides a FV annuity factor for various combinations of n (number of periods) and i (interest rate per period). By multiplying the FV annuity factor by the payment amount, we obtain the FV of the annuity. For example, with three payments of $100 at 15% interest, we can locate n = 3 and i = 15% in the table to find an FV factor of 3.4721. The future value of this annuity is: FV=100×3.4721=347.21FV = 100 3. Example Calculation: Suppose a company invests $45,000 annually over five years at 12% interest. Using the FV annuity factor for n = 5 and i = 12% (6.3528 from Table B.4), the future value is: FV=45,000×6.3528=285,876FV = 45,000 This amount represents the total accumulated value of the investment at the end of five years. 4. Important Distinctions in Annuity Tables: o o Table B.2 (Single Amount): Shows the FV for a single payment compounded over time. When n = 0, there is no interest, so the FV remains as the payment amount. Table B.4 (Annuities): Focuses on annuities, where n = 1 represents one payment, with the FV equal to that payment, as no time passes to accrue interest. Summary The FV of an annuity is a practical calculation for estimating the future worth of regular, equal payments with interest. Using FV annuity tables or formulas allows for quick calculations, supporting planning for future financial goals.