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Finance Calc Kit
Retirement

Growing Annuity Calculator

Calculate the present value, future value, and total payments of a growing annuity with customizable initial payment, growth rate, interest rate, and payment timing.

Growing annuity inputs

$
Quick amounts:
%
%
years

Present value of growing annuity (PVGA)

$4,457.43

Current lump-sum equivalent across 5 years with 3.0% annual payment growth discounted at 6.0%

Future value (FVGA)

$5,965.05

Compounded total by end of year 5

Total cash payments

$5,309.14

Final payment: $1,125.51

Total interest earned

$655.91

Compounded gain over nominal deposits

PV discount savings

$851.70

Difference between nominal payments and present value

Annuity due PV

$4,724.88

+$267.45 if paid at period start

Cash payments vs compounded growth

  • Total cash payments$5,309.1489.0%
  • Compounded interest growth$655.9111.0%

How the growing annuity is calculated

Mathematical breakdown for calculating present value and future value with constant geometric growth.

  1. Determine periodic rates and payment count

    r=6%1=6.0000%,g=3%1=3.0000%,n=5r = \frac{6\%}{1} = 6.0000\%, \quad g = \frac{3\%}{1} = 3.0000\%, \quad n = 5

    Across 5 compounding periods, the periodic discount/interest rate is 6.0000% and the payment growth rate is 3.0000%.

  2. Calculate Present Value (PVGA)

    PV=C1r−g[1−(1+g1+r)n]PV = \frac{C_1}{r - g} \left[ 1 - \left(\frac{1 + g}{1 + r}\right)^n \right]

    For ordinary end-of-period cash flows, discounting gives a present value of $4,457.43.

  3. Calculate Future Value (FVGA) and Total Payments

    FV=C1[(1+r)n−(1+g)nr−g]FV = C_1 \left[ \frac{(1 + r)^n - (1 + g)^n}{r - g} \right]

    Nominal escalating payments total $5,309.14, compounding into $5,965.05 at terminal maturity.

Payment & growth schedule

Yearly total payments, interest growth, ending future value, and present value equivalent.

YearYearly cash flowsPV equivalentYearly interestCompounded FV
Year 1$1,000.00$943.40$0.00$1,000.00
Year 2$1,030.00$916.70$60.00$2,090.00
Year 3$1,060.90$890.75$125.40$3,276.30
Year 4$1,092.73$865.54$196.58$4,565.61
Year 5$1,125.51$841.05$273.94$5,965.05
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Understanding growing annuities

A growing annuity is a finite stream of cash flows that expand at a constant percentage rate each period over a defined horizon. Unlike standard level annuities where every installment is identical, growing annuities account for regular payment increases driven by inflation, contractual escalation clauses, scheduled salary increments, or expanding dividend payouts.

This calculator evaluates both the present value (PVGA) and future value (FVGA) of escalating cash flows, supporting both ordinary annuities (end of period) and annuities due (start of period). If your cash flows remain constant without annual increases, evaluate level payments with our annuity calculator. When focusing exclusively on long-term terminal accumulation and compounded wealth, consult the future value of growing annuity calculator. For standard constant contributions where every deposit is invested on the first day of the billing cycle, compare returns using our future value of annuity due calculator. If you are evaluating a fixed-income retirement draw phase with level scheduled withdrawals, model your depletion timeline with the annuity payout calculator.

Growing annuity formulas

Let C₁ represent the initial payment received or deposited in period 1, g denote the periodic growth rate, r represent the periodic discount or interest rate, and n represent the total number of payment intervals.

Present value of an ordinary growing annuity (r ≠ g)

When the discount rate differs from the payment growth rate, the present value discounts each escalating payment back to time zero:

PV=C1r−g[1−(1+g1+r)n]\mathrm{PV} = \frac{C_1}{r - g} \left[ 1 - \left( \frac{1 + g}{1 + r} \right)^n \right]

Future value of an ordinary growing annuity (r ≠ g)

The future value compounds all escalating cash flows to the end of period n:

FV=C1[(1+r)n−(1+g)nr−g]\mathrm{FV} = C_1 \left[ \frac{(1 + r)^n - (1 + g)^n}{r - g} \right]

Special condition: when interest rate equals growth rate (r = g)

If the discount rate exactly matches the growth rate (r = g), the standard fraction yields a zero-denominator division. Taking the algebraic limit reveals that each cash flow discounted back to time zero simplifies to C₁ / (1 + r). Across n identical discounted periods:

PVr=g=n×C11+r,FVr=g=n×C1×(1+r)n−1\mathrm{PV}_{r=g} = \frac{n \times C_1}{1 + r}, \quad \mathrm{FV}_{r=g} = n \times C_1 \times (1 + r)^{n - 1}

Ordinary annuity vs. annuity due timing

Under an ordinary annuity, payments occur at the end of each payment period. Under an annuity due, payments occur at the beginning of each period. Because every cash flow occurs one compounding period earlier, both present value and future value are scaled by a factor of (1 + r):

PVdue=PVordinary×(1+r),FVdue=FVordinary×(1+r)\mathrm{PV}_{\text{due}} = \mathrm{PV}_{\text{ordinary}} \times (1 + r), \quad \mathrm{FV}_{\text{due}} = \mathrm{FV}_{\text{ordinary}} \times (1 + r)

Worked example: valuing a multi-year escalating contract

Suppose you are evaluating a 5-year commercial royalty or pension agreement where the initial year-end payment is $1,000. Each subsequent year, the payment increases by 3% to offset inflation, and the appropriate annual discount rate is 6%.

  • Initial payment (C₁): $1,000
  • Payment growth rate (g): 3.0% (0.03)
  • Discount rate (r): 6.0% (0.06)
  • Duration (n): 5 years

Step 1: Calculate the nominal cash payments across the 5 years:

YearPayment formulaCash payment
Year 1$1,000 × (1.03)⁰$1,000.00
Year 2$1,000 × (1.03)¹$1,030.00
Year 3$1,000 × (1.03)²$1,060.90
Year 4$1,000 × (1.03)³$1,092.73
Year 5$1,000 × (1.03)⁴$1,125.51
Total nominal cashSum of all 5 payments$5,309.14

Step 2: Apply the present value equation:

PV=10000.06−0.03[1−(1.031.06)5]=33,333.33×[1−0.866277]=$4,457.43\mathrm{PV} = \frac{1000}{0.06 - 0.03} \left[ 1 - \left(\frac{1.03}{1.06}\right)^5 \right] = 33{,}333.33 \times [1 - 0.866277] = \$4{,}457.43

Step 3: Calculate the compounded terminal future value:

FV=1000×[(1.06)5−(1.03)50.06−0.03]=1000×[1.338226−1.1592740.03]=$5,965.05\mathrm{FV} = 1000 \times \left[ \frac{(1.06)^5 - (1.03)^5}{0.06 - 0.03} \right] = 1000 \times \left[ \frac{1.338226 - 1.159274}{0.03} \right] = \$5{,}965.05

Notice that the relationship FV = PV × (1 + r)ⁿ holds exactly: $4,457.43 × (1.06)⁵ = $5,965.05. If you need to model arbitrary, irregular cash flow series that do not follow a constant growth rate, use our comprehensive discounted cash flow calculator.

Frequently asked questions

What is the primary difference between an annuity and a growing annuity?
In a standard annuity, every periodic payment is equal. In a growing annuity, each payment increases by a constant percentage rate (g) every period, helping reflect inflation or contractual increases.
Can the growth rate (g) exceed the discount rate (r)?
Yes. For finite horizons (a fixed number of years n), the formula remains valid whether g is less than, equal to, or greater than r. This differs from infinite growing perpetuities, which require r to be strictly greater than g to avoid infinite values.
What happens if the discount rate equals the growth rate (r = g)?
When r equals g, the general formula produces zero divided by zero. In that scenario, the calculator switches to the exact limit formula: PV = (n × C₁) / (1 + r) and FV = n × C₁ × (1 + r)^(n - 1).
How does payment frequency affect the calculation?
When selecting semi-annual, quarterly, or monthly payments, the calculator divides both the annual interest rate and the growth rate by the payment frequency factor, while multiplying the total years by the same factor to establish total compounding periods.
Does the calculator store or transmit my financial data?
No. All calculations run strictly in your web browser using client-side JavaScript. Updating values only alters the URL parameters so you can bookmark or share your scenario.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.