Future Value of Annuity Calculator

How to Calculate Future Value of Annuity

The future value of an annuity is a crucial concept in finance that helps individuals and businesses understand how a series of equal payments will grow over time when invested at a specific interest rate. This guide will walk you through the process of calculating the future value of an annuity.

Future Value of Annuity Formula

There are two main types of annuities: ordinary annuities and annuities due. The formulas for each are slightly different:

Ordinary Annuity (Payments at the end of each period):

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

Annuity Due (Payments at the beginning of each period):

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

Where:

• FV = Future Value of the Annuity
• PMT = Regular Payment Amount
• r = Interest Rate per Period
• n = Total Number of Periods

Calculation Steps

1. Determine the type of annuity (ordinary or due).
2. Identify the regular payment amount (PMT).
3. Calculate the interest rate per period (r) by dividing the annual interest rate by the number of compounding periods per year.
4. Calculate the total number of periods (n) by multiplying the number of years by the number of payments per year.
5. Apply the appropriate formula based on the annuity type.
6. Calculate the result to find the future value of the annuity.

Example Calculation

Let's calculate the future value of an ordinary annuity with the following characteristics:

• Regular Payment (PMT): $1,000
• Annual Interest Rate: 6%
• Number of Years: 10
• Payments Made: Annually (at the end of each year)

Step 1: Identify the variables

• PMT = $1,000
• r = 6% = 0.06 (annual rate, compounded annually)
• n = 10 years

Step 2: Apply the ordinary annuity formula

$$FV = 1000 \times \frac{(1 + 0.06)^{10} - 1}{0.06}$$

Step 3: Calculate the result

$$FV = 1000 \times \frac{1.7908 - 1}{0.06} = 1000 \times 13.1804 = $13,180.40$$

Therefore, the future value of this annuity after 10 years is $13,180.40.

Visual Representation

This line chart illustrates the growth of the annuity value over the 10-year period. As you can see, the value increases more rapidly in later years due to the compounding effect of interest.