Investment Calculator
Compute the future value, total principal and gains of a lump sum plus recurring contributions under compound interest.
Input Data
Results
At a glance:The Investment Calculator computes the future value of an initial principal plus recurring contributions under compound interest: FV = PV × (1 + r/m)^(mt) + contribution future value (end annuity). PV future value = PV × (1 + r/m)^(mt); contribution future value = PMT × [((1 + r/m)^(mt) − 1) ÷ (r/m)], where r is annual return, m the compounding frequency, t the years. Gains = FV − total principal. Suits long-term savings and recurring contributions (e.g. monthly stock/fund plans).
Formula
PV future value = PV × (1 + r/m)^(m·t).
Contribution future value (end annuity) = PMT × [((1 + r/m)^(m·t) − 1) ÷ (r/m)]; at r = 0 degenerates to PMT × m·t.
FV = PV future value + contribution future value; gains = FV − total principal.
$$FV = PV \left(1+\dfrac{r}{m}\right)^{mt} + PMT \cdot \dfrac{\left(1+\frac{r}{m}\right)^{mt}-1}{\frac{r}{m}}$$$$\text{Gains} = FV - (PV + PMT \times mt)$$How to Use
- Enter the initial principal and (optional) periodic contribution.
- Enter the expected annual return and holding years.
- Choose the compounding frequency to see FV, total principal and gains.
Future value examples by principal, contribution and term (compound)
| Initial | Contribution | Return | Term/compound | FV | Gains |
|---|---|---|---|---|---|
| HK$10,000 | HK$0 | 10% | 3y/yearly | HK$13,310 | HK$3,310 |
| HK$50,000 | HK$2,000/mo | 6% | 10y/monthly | HK$418,729 | HK$128,729 |
| HK$100,000 | HK$5,000/mo | 7% | 20y/monthly | HK$3,008,507 | HK$1,708,507 |
End annuity (contribution at period end). Long-run monthly contributions can yield gains far exceeding principal — in the 20-year case gains HK$1.71m exceed the HK$1.3m contributed, the power of compounding and time. Illustrative; actual returns fluctuate.
Case Studies
Case 1: Lump-sum compound growth
Mr Chan invests HK$10,000 once at 10% annual return, yearly compounding, 3 years (no contribution, PMT = 0).
Degenerates to PV compounding: FV = 10,000 × 1.10^3 = 10,000 × 1.331 = HK$13,310.
Gains = 13,310 − 10,000 = HK$3,310. Interest rolls into principal yearly (1,000 then 1,100 then 1,210) — compounding beats simple interest by HK$310.
Case 2: Long-run monthly contribution power
May invests HK$100,000 plus HK$5,000/month at 7% (monthly), for 20 years.
After 20 years (m = 12, t = 20, 240 periods) FV ≈ HK$3,008,507. Total principal = 100,000 + 5,000 × 240 = HK$1,300,000; gains ≈ HK$1,708,507 — exceeding the principal!
Lesson: the power of 'dollar-cost averaging + time + compounding'. Early gains are small but later yearly gains exceed that year's contribution as principal grows. Notes: (1) this uses end annuity (most common savings assumption); (2) 7% is illustrative, actual returns fluctuate; (3) use real return (inflation-adjusted) for today's purchasing power. Pair with the compound-interest and FIRE calculators.
FAQ
Are contributions at the beginning or end of the period?
This calculator uses the end-annuity convention — each contribution is added at the end of the compounding period. This is the most common savings/contribution assumption and matches most financial tools.
Does compounding frequency affect the result?
Yes. At the same nominal annual return, more frequent compounding means interest rolls into principal more often, so the FV is slightly higher. Over the long run this difference is magnified by time.
Can I invest a lump sum only, no contribution?
Yes. Set the periodic contribution to 0 for pure principal compounding; the formula degenerates to FV = PV × (1 + r/m)^(m·t).
How does this differ from the compound-interest and future-value calculators?
All three are compound-interest based and overlap heavily; the difference is whether recurring contributions are supported and the interface focus. (1) Investment Calculator (this tool) supports both initial principal and recurring contribution — best for simulating monthly stock/fund savings plans, showing FV, principal and gains. (2) Compound Interest Calculator focuses on compounding growth of a lump sum, good for comparing rates/frequencies. (3) Future Value Calculator is the general time-value tool, paired with PV. If you invest a lump sum only, all three agree (set contribution to 0).
What annual return should I enter; what about real volatility?
The calculator assumes a fixed yearly return, but real returns fluctuate. Use a reasonable conservative long-run average: diversified global equity ~7%–10% nominal / ~5%–7% real; balanced ~lower; bonds/deposits lower. Run conservative/neutral/optimistic scenarios, and use real return (nominal minus inflation) for purchasing power — pair with the real-rate-of-return calculator. Understand the result is an idealised average; volatility and sequence-of-returns risk matter, so diversify and hold long.
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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.