Annuity Payment Calculator

What is an Annuity?

An annuity is a financial product that provides a series of payments at regular intervals, typically for retirement income. It's a contract between you and an insurance company where you make a lump sum payment or series of payments, and in return, the insurer agrees to make periodic payments to you, beginning either immediately or at some point in the future.

The Annuity Payment Formula

The formula for calculating annuity payments depends on whether the payments are made at the beginning or end of each period:

For payments at the end of each period (ordinary annuity):

\[P = \frac{A \cdot r}{1 - (1 + r)^{-n}}\]

For payments at the beginning of each period (annuity due):

\[P = \frac{A \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}\]

Where:

• \(P\) = Periodic payment amount
• \(A\) = Present value (initial principal)
• \(r\) = Interest rate per period (in decimal form)
• \(n\) = Total number of periods

Step-by-Step Annuity Payment Calculation

1. Determine the initial principal (A), interest rate (r), number of periods (n), and whether payments are made at the beginning or end of each period.
2. Convert the interest rate to decimal form (divide by 100).
3. Choose the appropriate formula based on when payments are made.
4. Plug the values into the formula.
5. Calculate the periodic payment amount (P).

Example Calculation

Let's calculate the annual payment for an annuity with an initial principal of $100,000, an annual interest rate of 5%, paid out over 20 years, with payments at the end of each year:

1. \(A = \$100,000\), \(r = 5\% = 0.05\), \(n = 20\) years
2. Using the ordinary annuity formula: \[P = \frac{100000 \cdot 0.05}{1 - (1 + 0.05)^{-20}} = \$8,024.26\]

Visual Representation

The green portion represents the initial principal ($100,000), and the blue portion represents the total interest paid out over the 20-year period ($60,485).