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.