# Future Value of Annuity Calculator

## Future Value of Annuity Calculator

The future value of an annuity is the amount of money that an annuity will be worth at the end of a specified period, given a certain interest rate and payment schedule. An annuity is a series of equal payments made at regular intervals over time. The future value calculates how much these payments will grow to, considering the compound interest earned on each payment.

#### What a Future Value of Annuity Calculator Does:

**Inputs:****Payment Amount (P):**The amount of each regular payment or deposit.**Interest Rate (r):**The periodic interest rate (usually annual, but could be monthly, quarterly, etc.).**Number of Periods (n):**The total number of payments or periods over which the payments are made.**Compounding Frequency:**How often the interest is compounded (monthly, annually, etc.).

**Calculation:**- Uses the formula for the future value of an annuity to compute the total amount accumulated at the end of the investment period.

#### Future Value of an Annuity Formula:

The formula to calculate the future value of an annuity (FV) is:

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

Where:

– \( \text{FV} \) = Future Value of the annuity

– \( P \) = Payment amount per period

– \( r \) = Interest rate per period

– \( n \) = Total number of payments

#### Benefits of Using a Future Value of Annuity Calculator:

**Accuracy:**Ensures precise calculations without manual errors.**Time-Saving:**Quickly computes results, saving you from complex and time-consuming manual calculations.**Planning:**Helps in financial planning by showing how much your regular investments will grow over time.**Comparison:**Allows you to compare different investment scenarios by adjusting payment amounts, interest rates, and periods.

#### Example

Let’s say you want to calculate the future value of an annuity where you make monthly deposits of $200 into an account that earns an annual interest rate of 6%, compounded monthly, for 5 years.

Step-by-Step Calculation:

1. Identify the Variables:

– \( P \) (monthly payment) = $200

– Annual interest rate = 6% or 0.06

– Monthly interest rate \( r \) = Annual interest rate / 12 = 0.06 / 12 = 0.005

– Total number of payments \( n \) = Number of years × 12 = 5 × 12 = 60

2. Plug the Values into the Formula:

\[

\text{FV} = 200 \times \frac{(1 + 0.005)^{60} – 1}{0.005}

\]

3. Perform the Calculation:

– First, calculate \( (1 + 0.005)^{60} \):

\[

(1 + 0.005)^{60} \approx 1.34885

\]

– Subtract 1 from the result:

\[

1.34885 – 1 = 0.34885

\]

– Divide by the interest rate per period:

\[

\frac{0.34885}{0.005} = 69.77

\]

– Multiply by the payment amount:

\[

200 \times 69.77 \approx 13,954

\]

**Result**:

The future value of the annuity is approximately $13,954.

To find the future value of an annuity, you need to know the amount of each payment, the interest rate, and the number of payments. By using the formula \( \text{FV} = P \times \frac{(1 + r)^n – 1}{r} \), you can determine how much your series of payments will be worth at the end of the specified period.