Time Value of Money (TVM) Calculator
Compute the present value or future value including regular contributions (end-of-period annuity).
Input Data
Results
At a glance:Time Value of Money (TVM) is the foundation of personal finance and investing: because money can earn and be reinvested, the same amount is worth different amounts at different points in time — a dollar today is worth more than a dollar tomorrow. The TVM calculator combines a lump sum with regular contributions (end-of-period annuity) so you can convert between present value (PV) and future value (FV): solving for FV, you input the present principal and periodic contributions to get the accumulated amount after a number of periods; solving for PV, you input the future target and periodic contributions to back out the equivalent present value. It is the most common maths behind Hong Kong savings plans, contribution insurance, pensions and investment decisions.
Formula
Future value: FV = PV × (1 + r)^n + payment × [((1 + r)^n − 1) ÷ r].
Present value: PV = FV ÷ (1 + r)^n + payment × [(1 − (1 + r)^−n) ÷ r].
r is the periodic rate, n is periods; when r = 0 the annuity part reduces to payment × n.
$$FV = PV(1+r)^n + PMT \cdot \dfrac{(1+r)^n - 1}{r}$$$$PV = \dfrac{FV}{(1+r)^n} + PMT \cdot \dfrac{1-(1+r)^{-n}}{r}$$How to Use
- Choose the solve target (future value or present value).
- Enter the known principal, periodic rate and number of periods.
- Add a periodic contribution if any; the result shows instantly.
FAQ
How do I convert an annual rate to a per-period rate?
If you are using an annual rate but contributing monthly, the per-period rate is the annual rate ÷ 12, and the number of periods is the number of years × 12. For example, a 6% annual rate over 10 years means enter 0.5 as the per-period rate and 120 as the periods.
Are contributions at the start or end of each period?
This calculator uses an end-of-period annuity (contributions made at the end of each period), which is the most common assumption. If contributions are made at the start of each period, the actual amount would be slightly higher.
Why is a dollar today worth more than a dollar in the future?
Because a dollar received today can be deposited, invested or used to pay down debt immediately and grow over time, while a dollar received later misses that growth period and is also eroded by inflation. This is the core of TVM—bringing cash at different points in time onto a common footing via the interest rate so they can be compared fairly. With Hong Kong's long-run inflation around 2%–3%, this underscores the value of starting early.
What is the difference between present value (PV) and future value (FV)?
Future value answers 'if I deposit this now and contribute each period, how much will it grow to in N periods'—useful for savings and retirement planning. Present value answers 'if I need a certain amount in N periods, how much should I set aside today / what is that future income worth now'—useful for evaluating one-off goals, pensions or the today's value of future income. The two are inverse operations of each other.
How much does the interest rate affect the result?
Enormously, and it compounds with the number of periods. With a HK$100,000 lump sum, HK$2,000 monthly contribution and 0.5% per period (6% p.a.): at 60 periods (5 years) the future value is about HK$274,425, but at 240 periods (20 years) it is about HK$1,255,102. Quadrupling the periods more than quadruples the future value—that is the power of compounding plus regular contributions, showing why a long, early and consistent saving horizon matters.
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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.