Direct answer
To “join” a compound interest problem with forex, you map the idea of earning interest and compounding over time to the interest-rate component that affects currency returns. In practice, that means treating the position as a currency exposure whose expected growth is driven by an interest-rate differential (one currency’s interest rate versus the other), over a specific time horizon, under explicit assumptions.
How it works (mechanics and mapping)
Start with two simple building blocks:
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Compound interest (time compounding): A value can grow when interest is periodically added and then also earns interest. A basic way to express this is: growth depends on the interest rate, the compounding frequency (how often interest is added), and the holding time.
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Forex exposure (two rates): In forex you exchange one currency for another. Over time, the “carry” part of returns is often discussed as coming from the relative interest rates between the two currencies. Conceptually, if Currency A offers higher interest than Currency B (and if you hold the exposure long enough), the return contribution from interest can be seen as partially offsetting or enhancing any spot exchange-rate movement.
To combine them, you can structure the “compound interest” problem like this:
- Pick a start date, an end date, and an assumed holding period.
- Choose assumed interest rates for each currency for that horizon.
- Model growth of each currency amount using compounding (or an approximation if compounding details are unknown).
- Compare the resulting relative growth to see how interest-rate differences can translate into an expected currency return component.
A useful mental check is that the model should produce consistent results when you swap roles of the two currencies: the sign of the interest-rate differential flips, so the implied direction of the interest component should flip as well.
Example or checks (without promising outcomes)
Consider a simplified thought experiment with assumptions:
- You hold an amount equivalent to Currency A at the start.
- Currency A earns interest that compounds over the holding period.
- At the same time, Currency B would have its own compounding if you held it instead.
Then:
- The interest-rate differential determines how much faster (or slower) Currency A’s amount would grow compared to Currency B’s amount, given your assumptions.
- Any real forex result is still the sum of multiple drivers. Your “joined” compound-interest model captures one driver (interest-rate logic), not everything.
Independent verification you can do without forecasting:
- Check whether your model’s implied direction matches the sign of the assumed interest differential.
- Re-run the same structure with slightly different assumed rates to see sensitivity: if small rate changes reverse the effect, your joined problem is highly assumption-dependent.
Limitations and risks (what can break the model)
- Rates are not fixed: Real interest rates can change during the holding period, so a single assumed rate may not represent the whole path.
- Compounding assumptions may be wrong: Different market mechanics can use different effective frequencies or calculations, so the exact compounding frequency can change the result.
- Forex returns are not only interest: Exchange rates move for many reasons beyond interest, so the compound-interest mapping is incomplete.
- Execution constraints: Real trading involves costs and implementation details that can affect realized returns; a purely conceptual model may ignore these.
If you want the “joined” compound interest approach to be meaningful, you must clearly state assumptions (horizon, rate inputs, compounding rule) and treat the output as a reasoning tool rather than a prediction.