Compound interest calculator

Estimate the future balance of a starting amount plus a repeating contribution, at a fixed annual rate. Read the amounts as Hong Kong dollars, or as any other single currency. This page does not convert currencies.

Read how compound interest works

How this calculator works

The question it answers

It estimates a future balance from a starting amount, a fixed annual interest rate, and an optional contribution added at the end of every compounding period. The contribution frequency matches the compounding frequency.

The formula

When the interest rate per period (i) is not zero, the future value (FV) is:

FV = P × (1 + i)^n + PMT × [((1 + i)^n − 1) / i]

P: Principal, the amount you start with.
PMT: Contribution added at the end of each compounding period.
i: Annual rate divided by the number of compounding periods per year. A 6% annual rate compounded monthly is 0.5% per period.
n: Compounding periods per year, multiplied by the number of years.

When the rate is zero

A zero rate earns nothing. The future value is only what you put in:

FV = P + PMT × n

Interest earned

Interest earned is the future value minus the principal minus every contribution. Daily compounding uses 365 periods per year, including in leap years, so one year stays comparable with the next.

Checks you can do by hand

1,000 at 5% compounded once a year, for one year, with no contribution, is 1,050. 1,000 at 10% compounded annually for two years is 1,210. A zero rate never invents interest.

What it leaves out

Fees, taxes on returns, MPF contribution caps, and investment returns that move around are not included. An MPF fund is not a fixed interest rate. US dividends, fund expense ratios, and taxes are not deducted. The figure is an estimate for learning, not a quote and not advice.

Before you act, check the Inland Revenue Department, the Mandatory Provident Fund Schemes Authority, your bank, or a licensed adviser.

Worked example

The checks below use the formula on this page. Each row compounds once a year, so the period count is the number of years, and adds no contribution.

Principal	Annual rate	Compounding	Periods	Contribution	Future value
1,000	5%	Once a year	1	0	1,050
1,000	10%	Once a year	2	0	1,210

Questions

What does 1,000 at 5% become after one year?

1,000 at 5% compounded once a year, for one year, with no contribution, is 1,050. The worked example also shows 1,000 at 10% compounded annually for two years, which is 1,210.

How is the future value calculated?

When the interest rate per period is not zero, the future value grows the principal by (1 + i) for n periods and adds the end-of-period contributions on the same rate. i is the annual rate divided by the compounding periods per year, and n is those periods times the years. A 6% annual rate compounded monthly is 0.5% per period.

What happens when the rate is zero?

A zero rate earns nothing. The future value is only what you put in: the principal plus each contribution multiplied by the number of periods.

What does the result leave out?

Fees, taxes on returns, MPF contribution caps, and investment returns that move around are not included. The figure is an estimate for learning, not a quote and not advice.

Related guides

How compound interest works