How this instrument works
Covered interest rate parity says a currency's forward premium and the interest differential between two currencies must line up, or a trader could borrow one currency, convert it, invest in the other, and sell the proceeds forward for a riskless profit. This calculator runs that no-arbitrage condition in reverse: instead of computing the forward quote from two known interest levels, it takes the spot price, the quoted forward price, and one interest figure, and solves for what the market's own FX quotes imply about the other currency.
That inversion matters because forward and spot FX prices trade in size, minute by minute, on transparent screens, while a currency's short-term money-market deposit yield is sometimes thin, stale, or simply hard for an outsider to observe. A frontier-market treasury desk, a hedge fund macro analyst pricing a carry trade, or anyone auditing a quoted local figure against what the FX market is actually pricing turns to this backward reading rather than trusting a printed deposit quote at face value.
The result is not automatically the real deposit figure a bank would quote you; it is the number consistent with the observed spot, forward, and foreign inputs under a no-arbitrage assumption. Where the two diverge — where a country's actual money-market level sits well away from what this formula implies — capital controls, settlement risk, or a shortage of dealers willing to arbitrage the gap are usually the reason, and that gap is informative about how open a currency's markets really are.
- Enter the Spot exchange rate quoted for the pair today.
- Enter the Forward exchange rate the market is quoting for the same settlement date.
- Set the Foreign interest rate, % — the money-market figure you already know or trust for the other currency.
- Enter Days to forward date — the exact calendar days until the contract settles, not a rounded month.
- Read the Implied domestic interest rate, % the instrument backs out from those four figures.
Worked example — backing out a 5.015% implied domestic rate
Take the golden case: spot at 1.10, a quoted 90-day forward of 1.1055, and a foreign interest level of 3%. The day-count fraction is t = 90 ⁄ 360 = 0.25, so the foreign factor is 1 + 0.03 × 0.25 = 1.0075. Dividing forward by spot gives F ⁄ S = 1.005, multiplying by 1.0075 gives 1.0125375, subtracting 1 leaves 0.0125375, and dividing by t then multiplying by 100 returns a domestic figure of 5.015% — almost exactly two points above the foreign number for a two-point premium on the quote.
Hold the same spot, forward, and foreign level but stretch the settlement out to 180 days instead of 90, and the implied domestic figure falls to 4.015% rather than staying at 5.015%. The forward premium embedded in 1.1055 over 1.10 is fixed, but spreading that fixed premium over twice the time means it represents a smaller annualized differential — exactly the sensitivity a trader checks before reading too much into a single day-count assumption.
Questions
Why solve for the domestic rate instead of the forward quote?
Because the domestic figure is sometimes the least trustworthy number on the desk. Spot and forward FX quotes trade continuously and transparently, and a foreign money-market level may already be pinned down by a policy announcement; running the parity formula in reverse extracts what the FX market is implicitly pricing for the domestic side, without needing a separate deposit quote at all.
What does it mean if the calculator's figure does not match the quoted local rate?
It usually means the two markets are not perfectly arbitraged together. Capital controls, a thin pool of dealers willing to trade the pair, counterparty credit limits, or settlement-timing costs can all keep a country's actual deposit level away from the figure this formula backs out — the size of that gap is itself a rough measure of how freely money can move across that currency's border.
Does the formula assume compound interest?
No — it uses simple interest scaled by the day-count fraction t = days ÷ 360, the same money-market convention priced into the underlying forward and spot quotes. That matches how short-term deposits are actually quoted for most major currencies; a bond desk computing a compounded, annual-equivalent yield from the same four inputs would return a slightly different number.
Why does the implied rate change when I only change the days field?
Because the forward premium embedded in a fixed spot and forward pair gets annualized differently depending on how many days it is spread over. The same gap between a 1.10 spot and 1.1055 forward implies roughly 5.0% annualized over 90 days but only about 4.0% over 180 days — the identical quote reads as a smaller yearly differential the longer the contract runs.
Who actually runs this calculation instead of just reading a quoted figure?
Currency traders checking whether a quoted local deposit level is consistent with what the FX forward market is pricing, macro analysts sizing up a carry trade before an interest rate differential is confirmed by an official print, and anyone auditing a broker's forward quote against textbook parity all start from these same four numbers.
Can this number come out negative?
Yes — a negative implied domestic figure simply means the forward trades at enough of a discount to spot, relative to the foreign level and the day count, that the parity condition only balances below zero. It is arithmetically valid and occasionally observed in real markets; it is not a sign the calculator has made an error.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.