Bond Valuation: Future Value of Ordinary Annuity

Future Value of an Ordinary Annuity

Introduction:
In the world of finance, annuities play a significant role as investment vehicles and retirement planning tools. An annuity is a series of regular cash flows received or paid at equal intervals over a specified period. The future value of an ordinary annuity refers to the accumulated value of these periodic cash flows at a specific point in the future. Understanding the concept of the future value of an ordinary annuity is crucial for evaluating investment opportunities, planning for retirement, and making financial decisions.

Formula for Future Value of an Ordinary Annuity:
The future value (FV) of an ordinary annuity can be calculated using the following formula:

FV = P * [(1 + r)^n - 1] / r

Where:
FV = Future value of the annuity
P = Periodic payment amount
r = Interest rate per period
n = Number of periods

Example 1:
Let's consider an example to illustrate the calculation of the future value of an ordinary annuity. Suppose you plan to invest $1,000 at the end of each year in an investment vehicle that offers an annual interest rate of 6%. The investment will be made for a period of 5 years. Using the formula mentioned above, we can calculate the future value of this annuity:

P = $1,000 (annual payment)
r = 6% (interest rate per period)
n = 5 (number of years)

FV = $1,000 * [(1 + 0.06)^5 - 1] / 0.06
FV = $1,000 * [1.33822 - 1] / 0.06
FV = $1,000 * 0.33822 / 0.06
FV ≈ $5,637.00

Therefore, at the end of the 5-year period, the future value of this ordinary annuity would be approximately $5,637.00.

Example 2:
Now, let's consider a scenario where you plan to save for retirement. You decide to contribute $500 at the end of each month to a retirement account that offers a 8% annual interest rate. Your goal is to accumulate enough funds to retire comfortably in 30 years. Using the future value formula, we can calculate the future value of this ordinary annuity:

P = $500 (monthly payment)
r = 8% / 12 = 0.0067 (interest rate per month)
n = 30 * 12 = 360 (number of months)

FV = $500 * [(1 + 0.0067)^360 - 1] / 0.0067
FV ≈ $1,060,513.70

In this case, after consistently contributing $500 per month for 30 years, the future value of this ordinary annuity would be approximately $1,060,513.70 at the time of retirement.

Conclusion:
The future value of an ordinary annuity is a fundamental concept in finance that helps assess the worth of a series of regular cash flows over time. By understanding how to calculate the future value, individuals can make informed investment decisions, plan for retirement, and set financial goals. The formula presented in this section allows for precise calculations, enabling investors to evaluate the potential growth of their annuities and make sound financial plans.

This article takes inspiration from a lesson found in FIN 4243 at the University of Florida.