Chartered Financial Analyst specializing in retirement planning, investment growth modeling, and time value of money.
The **Future Value of Growing Annuity Calculator** helps you forecast the future value of a series of payments that increase at a constant rate each period. This is essential for accurate retirement and long-term savings planning. Enter values for exactly four core parameters to solve for the missing one.
Future Value of Growing Annuity Calculator
Instructions: Enter values for exactly four core parameters to solve for the missing one.
Annuity Parameters
Future Value of Growing Annuity Formula
General Case (when $\mathbf{R} \ne \mathbf{G}$):
$$FV = PMT_1 \times \left[ \frac{(1+R)^N – (1+G)^N}{R – G} \right]$$Special Case (when $\mathbf{R} = \mathbf{G}$):
$$FV = PMT_1 \times N \times (1+R)^{N-1}$$ Formula Source: InvestopediaVariables Explained ($\mathbf{PMT_1}, \mathbf{FV}, \mathbf{R}, \mathbf{N}, \mathbf{G}$)
- $\mathbf{PMT_1}$ ($Q$): The amount of the first periodic payment (e.g., deposit at end of year 1).
- $\mathbf{FV}$ ($F$): The total compounded value of all payments at the end of the term.
- $\mathbf{R}$ (Interest Rate, $P$): The annual rate of return earned on the investment (as a decimal).
- $\mathbf{G}$ (Growth Rate): The annual rate at which the periodic payment ($\mathbf{PMT}$) increases (as a decimal).
- $\mathbf{N}$ (Number of Years, $V$): The total number of years (periods) over which payments are made.
Related Annuity Calculators
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What is Future Value of a Growing Annuity?
A **Future Value of a Growing Annuity** is the total value of a sequence of increasing payments or cash flows at a specified future date, assuming a constant rate of return. This model is highly relevant for retirement planning because most people anticipate their contributions (like 401k or IRA payments) will increase as their salary grows. By incorporating the payment growth rate ($G$), the calculation provides a much more realistic forecast of a long-term savings goal than a standard annuity calculation which assumes fixed payments.
For example, if you start contributing \$5,000 per year, but expect your contribution to increase by 3% annually, the growing annuity model accounts for both the interest earned on your investments ($R$) and the increased principal contributions over time.
How to Calculate Future Value of a Growing Annuity (Example)
Imagine the first annual deposit ($\mathbf{PMT_1}$) is \$1,000, the investment term ($\mathbf{N}$) is 10 years, the annual interest rate ($\mathbf{R}$) is 8% (0.08), and the payment growth rate ($\mathbf{G}$) is 3% (0.03).
- Step 1: Determine the Differential Rate ($R – G$)
$$R – G = 0.08 – 0.03 = \mathbf{0.05}$$
- Step 2: Calculate the Numerator Component
Calculate $\text{Numerator} = (1+R)^N – (1+G)^N = (1.08)^{10} – (1.03)^{10} \approx 2.158925 – 1.343916 = \mathbf{0.815009}$
- Step 3: Calculate the Annuity Factor
$$\text{Factor} = \frac{\text{Numerator}}{R – G} = \frac{0.815009}{0.05} \approx \mathbf{16.3002}$$
- Step 4: Calculate the Future Value
$$\mathbf{FV} = \mathbf{PMT_1} \times \text{Factor} = \$1,000 \times 16.3002 = \mathbf{\$16,300.20}$$
The Future Value of the growing annuity is $\mathbf{\$16,300.20}$.
Frequently Asked Questions (FAQ)
$R$ is the return you earn on your investment portfolio, typically set by the market. $G$ is the rate at which you increase your personal contribution (the payment) each period, typically tied to expected salary increases.
The general formula breaks down due to division by zero. In this special case ($R=G$), a simplified linear formula is used: $\mathbf{FV} = \mathbf{PMT_1} \times N \times (1+R)^{N-1}$.
It helps set more accurate contribution targets. Planners can use the calculator to solve for the required initial payment ($PMT_1$) needed today to hit a large retirement goal ($FV$), assuming their income (and thus payments) will grow by $G$.
Yes. Due to the complexity of the $R$ and $N$ variables being locked within exponents, the calculation requires iterative methods (like the Bisection Method), which the robust JavaScript in this module is designed to handle.