Annuity Calculator

Understanding Annuity Accumulation

An annuity is a financial product designed to provide a steady stream of payments in the future, commonly used as a tool for retirement planning. During the accumulation phase, you build up the value of the annuity through a combination of starting principal, periodic contributions, and tax-deferred growth.

Annuity Due vs. Ordinary Annuity

One of the most important options to select when setting up an annuity is whether additions are deposited at the start or the end of each payment period:

• Annuity Due (Beginning of Period): Contributions are made at the beginning of each period. Because the funds are deposited earlier, they have more time to earn interest, resulting in a higher final balance.
• Ordinary Annuity (End of Period): Contributions are made at the end of each period. This is standard for many retirement accounts where payroll deductions happen at the end of a pay cycle.

Mathematical Growth Formulas

To forecast the growth of an annuity, we use the following standard formulas for future value (FV) under constant compounding:

• Future Value of an Ordinary Annuity: $$FV = PMT \times \frac{(1 + r)^n - 1}{r}$$
• Future Value of an Annuity Due: $$FV = PMT \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$$

Where $PMT$ is the payment amount per period, $r$ is the interest rate per period, and $n$ is the total number of periods.