Compound Interest Calculator
Calculate compound interest growth: enter the initial principal and monthly contribution to estimate the future value, cumulative interest and contributions.
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Compound growth: contributions vs interest
Chart notes:At the same rate, a longer term produces a much larger final amount because interest itself earns interest; the later years contribute far more growth than the early ones. Adding a monthly contribution raises the final value further, showing the power of time and discipline.
At a glance:Compound interest adds each period's interest to the principal so that the next period earns interest on the enlarged balance — 'interest on interest'. The core formula is FV = P × (1 + r)^n, where P is principal, r is the periodic rate and n is the number of periods. Monthly contributions use the future value of an ordinary annuity: FV = PMT × [((1 + r)^n − 1) ÷ r].
Formula
Principal compounded: FV = P × (1 + r)^n, r monthly rate (annual ÷ 12), n total months.
Monthly contribution (ordinary annuity): FV = PMT × [((1 + r)^n − 1) ÷ r].
Cumulative interest = future value − total contributed.
$$FV = P(1+r)^n$$$$FV_{PMT} = PMT \times \dfrac{(1+r)^n - 1}{r}$$How to Use
- Enter the initial principal and monthly contribution (regular savings).
- Set the expected annual rate and term.
- The future value, total contributed and cumulative interest show instantly on the right.
Growth at 4% compounded monthly, starting from HK$100,000 with no extra contributions
| Years | Future value (HK$) | Total contributed (HK$) | Cumulative interest (HK$) |
|---|---|---|---|
| 1 | 104,069 | 100,000 | 4,069 |
| 5 | 122,099 | 100,000 | 22,099 |
| 10 | 149,087 | 100,000 | 49,087 |
| 20 | 222,252 | 100,000 | 122,252 |
| 30 | 331,091 | 100,000 | 231,091 |
Based on monthly compounding; actual returns fluctuate.
Case Studies
Case 1: Lump-sum time deposit
HK$100,000 at 4% compounded monthly for 10 years → about HK$149,087, of which HK$49,087 is interest — nearly half the principal. This illustrates the power of compounding over time.
Case 2: Monthly saving
HK$1,000 a month at 6% for 20 years (240 months) → about HK$462,041, with HK$240,000 contributed and HK$222,041 interest. Steady saving plus time can beat a one-off lump sum.
FAQ
What is the difference between simple and compound interest?
Simple interest is charged only on the principal each period; compound interest is 'interest on interest' — each period's interest is added to the principal and earns further interest. Over time compound interest grows much faster. Over 20–30 years at 4%–6%, most of the final value is interest, not the original principal.
Why does monthly compounding beat annual compounding?
At the same nominal annual rate, more frequent compounding gives a higher effective rate. Monthly compounding credits interest 12 times a year, so the next month already earns on the prior interest. The effective annual rate = (1 + nominal/12)^12 − 1, slightly above the nominal rate; the gap widens with higher rates and longer terms.
How is the monthly contribution (annuity) formula used?
The monthly contribution uses the future value of an ordinary annuity FV = PMT × [((1 + r)^n − 1) ÷ r], where r is the monthly rate (annual ÷ 12) and n the number of months. It is essentially many small deposits compounded to the end date. This tool adds it to the lump-sum part.
What rate should I use in Hong Kong?
It depends on the product: HK HKD time deposits are roughly 3%–4% recently; long-term equity index funds have historically returned about 7%–8% (with volatility, not guaranteed); bond funds are lower. Use a conservative rate for planning and do not blindly plug in past highs.
Are the results guaranteed?
No. This is a mathematical projection assuming a fixed rate; real deposits and investments fluctuate with the market and rates. The figures are for reference and education, not investment advice. ⚠️
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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.