Growing Annuity Calculator
Compute the future value of an annuity whose contributions rise by a fixed rate each year, with cumulative contributions and interest earned.
Input Data
Results
At a glance:A growing annuity has contributions that rise by a fixed rate each year. Year y contribution = first-year × (1 + g)^(y−1); end-of-period balance = prior × (1 + r) + current contribution, r = return, g = contribution growth. It fits reality — income usually rises with tenure and inflation, so you can save more. At g = 0 it reduces to a level ordinary annuity. The calculator shows future value, cumulative contributions and interest earned.
Formula
C_y = C_1 × (1 + g)^(y−1).
B_y = B_(y−1) × (1 + r) + C_y, B_0 = 0.
Total contributions = Σ C_y; interest = FV − contributions.
$$C_y = C_1 (1 + g)^{y-1}$$$$B_y = B_{y-1}(1 + r) + C_y, \quad B_0 = 0$$How to Use
- Enter the first-year contribution.
- Enter the annual return, the annual contribution growth and the years.
- View future value, total contributions and interest.
First 10,000, return 6%, 5 years, future value by growth rate
| Growth rate | Total contributions | Future value | Interest |
|---|---|---|---|
| 0% (level) | HK$50,000 | HK$56,371 | HK$6,371 |
| 3% (growing) | HK$53,091 | HK$59,651 | HK$6,559 |
Same 10k start, 6% return, 5 years: raising contributions 3%/yr lifts total from 50k to ~53k and FV from ~56k to ~60k. Higher g and longer term widen the gap vs level.
Case Studies
Case 1: Five years of salary-linked contributions
Mr Chan: first-year 10,000, +3% each year with raises, 6% return, 5 years (end-of-period).
Contributions: 10,000 / 10,300 / 10,609 / 10,927 / 11,255, total ≈ 53,091. Compounding (balance × 1.06 + contribution) → FV ≈ 59,651, interest ≈ 6,559.
Growing contributions put more in later; with compounding, five years ≈ 59.7k — closer to 'income rises yearly' than a flat plan.
Case 2: Growing vs level contributions
Same but fixed 10,000/yr (g = 0): total = 50,000, FV ≈ 56,371, interest ≈ 6,371.
Growing 3% contributes ~3,091 more, FV ~3,280 more. Small over 5 years, but over 20–30 (retirement) the later-year base is far higher, so the gap vs level is huge.
Notes: set g to a realistic raise/inflation, not over-optimistic; annual end-of-period, fixed r and g; nominal FV ignores inflation — plan in real terms. Pair with the annuity, retirement-savings and future-value calculators.
FAQ
Why grow contributions yearly?
Because real income usually rises with tenure and inflation, so affordable savings rise too. Growing contributions let you save more as capacity grows, accumulating notably more than fixed, and help offset inflation's erosion of purchasing power.
What if growth rate is 0?
Growth 0 means a fixed contribution each year — it reduces to a level ordinary annuity. Set g = 0 as a baseline to see how much more rising contributions accumulate.
Return vs growth rate — which matters more?
Both matter. The return compounds the whole balance (more so over long horizons); the growth rate lifts later contributions' base. Generally over long periods the return's compounding dominates, but steady rising contributions supply more principal to compound.
Growing annuity vs level annuity vs growing perpetuity?
Annuity = a series of periodic cash flows, split by whether contributions grow, and whether there is a term. (1) Level/ordinary annuity: fixed contribution each period, the basic form (this calculator with g = 0). (2) Growing annuity (this): contributions rise by a fixed rate yearly — closer to reality as income grows. It needs both g and r. (3) Growing perpetuity: same rising pattern but no end — used in valuation theory (e.g. Gordon Growth Model: value = next dividend ÷ (discount − growth), requiring discount > growth), computing a present value, not a finite future value. Also note ordinary (end-of-period) vs annuity due (beginning) — beginning contributions compound one extra period, so a slightly higher FV. This calculator uses end-of-period. Pick by whether contributions are fixed (level), rising with salary/inflation over a set term (growing annuity), or a perpetual cash flow for valuation (perpetuity). Pair with the annuity and future-value calculators.
How high should the contribution growth be; risks of too high?
The growth rate g decides how much contributions rise each year; set a realistic, sustainable number or you overstate future accumulation. Benchmark it to (1) expected raise — if saving from salary, set g near your realistic annual raise (e.g. 3%–5%); (2) inflation — if you only want to keep real purchasing power, set g near long-run inflation (HK low single digits). Be conservative (the lower of the two). Risks of too high: at, say, 10% over 20 years, year-20 contribution reaches ~61,000 from a 10,000 start — may exceed what future income can fund, making the pretty FV rest on an unrealistic assumption. Practical tips: use a conservative g; check later-year contributions are affordable; g need not equal r (independent parameters); if income is unstable, use 0 or very low g; remember nominal FV ignores inflation, so think in real terms for long goals. Pair with the retirement-savings and inflation calculators.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.