Future Value Of A Growing Annuity Calculator

Growing Annuity Future Value Formula:

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

Periodic Payment (PMT):

Interest Rate (r):

Growth Rate (g):

Number of Periods (n):

periods

Future Value (FV):

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1. What is a Growing Annuity?

A growing annuity is a series of periodic payments that increase at a constant growth rate each period. This calculator computes the future value of such an annuity, accounting for both the interest earned and the growth in payments.

2. How Does the Calculator Work?

The calculator uses the growing annuity future value formula:

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

Where:

\( PMT \) — Initial periodic payment amount
\( r \) — Interest rate per period (as a decimal)
\( g \) — Growth rate of payments per period (as a decimal)
\( n \) — Number of periods

Explanation: The formula accounts for both the compounding of interest and the growth of payments over time. The numerator calculates the difference between the growth of invested amounts and the growth of payments, while the denominator adjusts for the rate difference.

3. Importance of Growing Annuity Calculation

Details: Understanding growing annuities is crucial for financial planning, especially for scenarios like retirement planning with increasing contributions, salary growth models, or business revenue projections with growth.

4. Using the Calculator

Tips: Enter the initial payment amount, interest rate (as percentage), growth rate (as percentage), and number of periods. All values must be positive, and the interest rate should not equal the growth rate.

5. Frequently Asked Questions (FAQ)

Q1: What happens if growth rate equals interest rate?
A: The formula becomes undefined (0/0). In this special case, the formula simplifies to FV = PMT × n × (1 + r)^(n-1).

Q2: What are typical applications of growing annuities?
A: Retirement plans with increasing contributions, salary growth models, dividend growth investments, and business revenue projections.

Q3: How does payment frequency affect the calculation?
A: The interest rate and growth rate should match the payment period (annual, monthly, etc.), and n should be total number of periods.

Q4: What's the difference between ordinary and due growing annuities?
A: For payments at the beginning of each period (annuity due), multiply the result by (1 + r).

Q5: Can this be used for decreasing payments?
A: Yes, simply use a negative growth rate (though mathematically valid, ensure it makes sense for your scenario).