Annuity Payment Calculator

What is an Annuity Payment?

An annuity payment is a fixed sum of money paid to someone each year, typically for the rest of their life. In financial terms, it's a series of equal payments made at regular intervals over a specified period. Annuities are often used in retirement planning, insurance settlements, or loan repayments.

The Annuity Payment Formula

The formula for calculating annuity payments is:

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

Where:

• \(P\) = Periodic payment
• \(L\) = Loan amount (principal)
• \(r\) = Periodic interest rate (annual rate divided by the number of payments per year)
• \(n\) = Total number of payments

Step-by-Step Annuity Payment Calculation

1. Identify the principal amount (L), annual interest rate (r), and the number of years (n).
2. Convert the annual interest rate to decimal form (divide by 100).
3. If payments are made more frequently than annually, adjust r and n accordingly.
4. Plug these values into the annuity payment formula.
5. Calculate the periodic payment (P).

Example Calculation

Let's calculate the annual payment for an annuity with a principal of $100,000, an annual interest rate of 5%, over 20 years:

1. \(L = \$100,000\), \(r = 5\% = 0.05\), \(n = 20\) years
2. \(P = 100000 \times \frac{0.05(1+0.05)^{20}}{(1+0.05)^{20}-1} = \$8,024.26\)

Visual Representation

The green portion represents the principal ($100,000), and the blue portion represents the total interest paid ($60,485.20) over the 20-year period.