# Present Value of Annuity Calculator

## Present Value of Annuity Calculator

The present value of an annuity is the current worth of a series of future payments, given a specific interest rate. This concept helps in determining how much a series of future payments is worth in today’s terms, considering the time value of money. It is widely used in finance for evaluating investment opportunities, loans, retirement plans, and other financial products.

\[ \text{PV} = P \times \frac{1 – (1 + r)^{-n}}{r} \]

Where:

– \( \text{PV} \) = Present Value of the annuity

– \( P \) = Payment amount per period

– \( r \) = Interest rate per period

– \( n \) = Total number of payments

#### Example

Let’s say you want to find out the present value of an annuity where you will receive $500 at the end of each year for the next 10 years, and the annual interest rate is 5%.

#### Step-by-Step Calculation:

1. Identify the Variables:

– \( P \) (annual payment) = $500

– Annual interest rate \( r \) = 5% or 0.05

– Total number of payments \( n \) = 10

2. Plug the Values into the Formula:

\[

\text{PV} = 500 \times \frac{1 – (1 + 0.05)^{-10}}{0.05}

\]

3. Perform the Calculation:

– First, calculate \( (1 + r)^{-n} \):

\[

(1 + 0.05)^{-10} = (1.05)^{-10} \approx 0.61391

\]

– Subtract this result from 1:

\[

1 – 0.61391 = 0.38609

\]

– Divide by the interest rate per period:

\[

\frac{0.38609}{0.05} = 7.7218

\]

– Multiply by the payment amount:

\[

500 \times 7.7218 = 3,860.9

\]

**Result**:

The present value of receiving $500 annually for 10 years at an annual interest rate of 5% is approximately $3,860.90.

To determine the present value of an annuity, you need to know the payment amount per period, the interest rate per period, and the total number of payments. By using the formula \( \text{PV} = P \times \frac{1 – (1 + r)^{-n}}{r} \), you can find out how much a series of future payments is worth in today’s terms. This helps in making informed financial decisions and evaluating different investment opportunities.