Annuity Calculator

How to Calculate Annuities

Calculating annuities is an essential skill in financial planning and investment analysis. This guide will walk you through the process of determining the future value, present value, and payout of an annuity.

Annuity Formulas

The formulas used for annuity calculations are:

1. Future Value of an Ordinary Annuity:

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

2. Future Value of an Annuity Due:

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

3. Present Value of an Ordinary Annuity:

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

4. Present Value of an Annuity Due:

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

5. Payout of an Ordinary Annuity:

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

6. Payout of an Annuity Due:

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

Where:

• FV = Future Value
• PV = Present Value
• P = Payment amount (for future/present value) or Principal (for payout)
• 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 (future value, present value, or payout).
2. Identify the known variables: principal/payment amount, interest rate, time period, 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 time (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 future value of an ordinary annuity with the following terms:

• Payment (P) = $1,000
• Annual Interest Rate = 6%
• Time = 5 years
• Payment Frequency = Monthly (12 times per year)

Step 1: Calculate the periodic interest rate

$$r = \frac{6\%}{12} = 0.5\% = 0.005$$

Step 2: Calculate the number of periods

$$n = 5 \times 12 = 60 \text{ periods}$$

Step 3: Apply the future value formula for an ordinary annuity

$$FV = 1000 \times \frac{(1 + 0.005)^{60} - 1}{0.005}$$

Step 4: Calculate the result

$$FV = 1000 \times 64.48 = $64,480$$

Result: The future value of this annuity after 5 years is $64,480.

Visual Representation

This diagram illustrates how the value of a $1,000 monthly annuity grows over 5 years with a 6% annual interest rate. The curve shows the exponential growth of the annuity value due to compound interest.