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.
Chapter 25: Future Value of an Annuity
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