Growing Annuities Calculator

Growing Annuities Formula:

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

Payment (PMT):

Interest Rate (r):

Growth Rate (g):

Number of Periods (n):

periods

Future Value (FV):

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1. What is the Growing Annuities Formula?

The Growing Annuities formula calculates the future value of a series of payments that grow at a constant rate each period. It is commonly used in finance to evaluate investments with growing cash flows.

2. How Does the Calculator Work?

The calculator uses the Growing Annuities formula:

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

Where:

$ PMT $ — Initial payment amount ($)
$ r $ — Interest rate per period (%)
$ g $ — Growth rate per period (%)
$ n $ — Number of periods

Explanation: This formula accounts for both the compounding of interest and the growth of payments over time, providing the future value of the growing annuity stream.

3. Importance of Growing Annuities Calculation

Details: Calculating the future value of growing annuities is essential for financial planning, investment analysis, retirement planning, and evaluating projects with increasing cash flows.

4. Using the Calculator

Tips: Enter the initial payment amount in dollars, interest rate and growth rate as percentages, and the number of periods. All values must be positive, and the interest rate must not equal the growth rate.

5. Frequently Asked Questions (FAQ)

Q1: What is a growing annuity?
A: A growing annuity is a series of payments that increase at a constant rate each period over a fixed time frame.

Q2: When should I use the growing annuity formula?
A: Use this formula when evaluating investments, retirement plans, or any financial product with payments that grow over time.

Q3: What happens if the growth rate equals the interest rate?
A: The formula becomes undefined when r = g. In this special case, a different formula should be used: FV = PMT × n × (1 + r)^(n-1)

Q4: Can the growth rate be higher than the interest rate?
A: Yes, but this may result in rapidly increasing payments that could affect long-term sustainability of the annuity.

Q5: How does compounding frequency affect the calculation?
A: The formula assumes periods match the compounding frequency. For different compounding, adjust the rate and periods accordingly.