Annuity Payout Calculator

How to Calculate Annuity Payouts

Calculating annuity payouts is a crucial skill in financial planning and retirement analysis. This guide will walk you through the process of determining the payment amount or payout length of an annuity.

Annuity Payout Formulas

The formulas used for annuity payout calculations are:

1. Payment Amount for an Ordinary Annuity:

   $$P = PV \times \frac{r}{1 - (1 + r)^{-n}}$$

2. Payment Amount for an Annuity Due:

   $$P_{due} = PV \times \frac{r}{1 - (1 + r)^{-n}} \times \frac{1}{1 + r}$$

3. Payout Length:

   $$n = \frac{\log(1 - \frac{PV \times r}{P})}{\log(1 + r)}$$

Where:

• P = Payment amount
• PV = Present Value
• r = Periodic interest rate
• n = Number of periods

Calculation Steps

1. Determine the type of annuity (ordinary or due) and the calculation you want to perform (payment amount or payout length).
2. Identify the known variables: present value, interest rate, payout length (or payment amount), and payment frequency.
3. Calculate the periodic interest rate by dividing the annual rate by the number of payments per year.
4. Calculate the total number of periods by multiplying the payout length (in years) by the number of payments per year.
5. Apply the appropriate formula based on the annuity type and calculation desired.
6. Perform the calculation to obtain the result.

Example Calculation

Let's calculate the payment amount for an ordinary annuity with the following terms:

• Present Value (PV) = $100,000
• Annual Interest Rate = 5%
• Payout Length = 10 years
• Payment Frequency = Monthly (12 times per year)

Step 1: Calculate the periodic interest rate

$$r = \frac{5\%}{12} = 0.4167\% = 0.004167$$

Step 2: Calculate the number of periods

$$n = 10 \times 12 = 120 \text{ periods}$$

Step 3: Apply the payment formula for an ordinary annuity

$$P = 100000 \times \frac{0.004167}{1 - (1 + 0.004167)^{-120}}$$

Step 4: Calculate the result

$$P = 100000 \times 0.01060746 = $1,060.75$$

Result: The monthly payment for this annuity is $1,060.75.

Visual Representation

This diagram illustrates how the balance of a $100,000 annuity decreases over 10 years with monthly payments of $1,060.75 and a 5% annual interest rate. The curve shows the gradual reduction of the annuity balance due to regular payments and interest accrual.