Future Value of Annuity Calculator

What is a Future Value of Annuity?

The Future Value of Annuity is a financial concept that calculates the total value of a series of equal payments at a future date, given a specified interest rate. This concept is crucial in various financial planning scenarios, such as retirement planning, investment strategies, and loan repayments.

The Future Value of Annuity Formula

The formula for calculating the Future Value of Annuity is:

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

Where:

• $FV$ = Future Value
• $PMT$ = Annuity Payment (made at the end of each period)
• $r$ = Interest rate (in decimal form)
• $n$ = Number of periods

Step-by-Step Future Value of Annuity Calculation

1. Identify the annuity payment (PMT), interest rate (r), and number of periods (n).
2. Convert the interest rate to decimal form (divide by 100).
3. Calculate $(1+r{)}^n$.
4. Subtract 1 from the result in step 3.
5. Divide the result from step 4 by r.
6. Multiply the result from step 5 by PMT to get the Future Value.

Example Calculation

Let's calculate the Future Value of Annuity for an annual payment of $5,000, an interest rate of 5% per year, over 10 years:

1. $PMT=\mathrm{\$}5,000$, $r=5\mathrm{\%}=0.05$, $n=10$ years
2. $FV=5000\times \frac{(1+0.05{)}^{10}-1}{0.05}$
3. $FV=5000\times \frac{1.6288-1}{0.05}=5000\times 12.5779$
4. $FV=\mathrm{\$}62,889.46$

Visual Representation

The green portion represents the total investment ($50,000), and the blue portion represents the growth ($12,889.46).