What your instalment works out to

How the tool works it out

The purchase fee comes off each instalment first. The rest is invested and grows until the end of the term. The annual assumption becomes a monthly factor using the formula (1 plus p) to the power of one twelfth, minus 1. Every single instalment grows for exactly as many months as it has left until the end, so the first one grows longest. That is the standard annuity formula for payments made at the start of each period. With an assumption of 0 per cent, what remains at the end is exactly the sum of the deposits minus the fees, which shows you what the fee alone costs. The calculator always shows all three presets at once, so the range stays visible and not just the pleasant case. The line under the chart adds a setback: the price falls 50 per cent over the last twelve months while the instalments carry on.

What a savings plan can do and what it cannot

Anyone investing the same amount every month buys few units when prices are high and many when they are low. The average purchase price therefore sits below the average of the prices. This averaging effect smooths the moment of entry. It does not reduce market risk: if the price falls and stays down, the result falls with it, across every unit bought up to that point.

How fast that can happen was set out with figures by the European Central Bank in a post of 30 November 2022: the bitcoin price fell from around 69,000 US dollars in November 2021 to around 17,000 US dollars in mid-June 2022, and briefly below 16,000 US dollars after the insolvency of a large trading venue in November 2022. That is a drop of more than three quarters in seven months. The European Supervisory Authorities EBA, ESMA and EIOPA had already warned jointly in March 2022: many crypto-assets are highly risky and speculative, consumers must be prepared to lose all the money they put in, and the protections of EU financial market rules mostly do not apply to crypto-assets.

Fees, tax and where the calculator stops

The calculator knows only one kind of cost, the percentage purchase fee per instalment. In practice further costs come on top, and you have to add those up yourself.

For tax, every single instalment counts as its own purchase with its own period. Under section 23(1) no. 2 of the German Income Tax Act (Einkommensteuergesetz), the gain from a private disposal is taxable if no more than one year lies between acquisition and sale. Section 23(3) sentence 5 adds an exemption limit: gains stay tax free if the total gain from all private disposals in the calendar year is less than 1,000 euro. A savings plan running ten years produces 120 instalments with 120 different dates, and that needs proper records. These rules apply in Germany; readers elsewhere are taxed under their own country's rules.

The calculator assumes a constant annual return. No price behaves like that. Real paths jump, and the order of the good and bad years changes the result considerably, because late losses hit a larger holding than early ones. Inflation, tax, exchange rates and the question of whether the chosen trading venue still exists in ten years are left out as well. So the tool answers a single question: what does this instalment produce arithmetically under this assumption. It does not answer whether the assumption holds.

Frequently asked questions

Sources