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Forward Rate Calculator

Solve the covered-interest-parity relationship for the forward rate, quote-currency rate, or base-currency rate from spot, tenor, and the remaining inputs.

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Solve the covered-interest-parity relationship Choose whether to solve for the forward rate, the quote-currency rate, or the base-currency rate. Rates are annual simple percentages and the spot quote should be entered as quote currency per one base currency.

Solve for

Assumptions

The solver uses a simple-rate covered-interest-parity identity over the entered term. It does not adjust for day-count conventions, broken dates, collateral basis, transaction costs, or non-deliverable-forward pricing differences.

Result

1.110837

Implied forward rate from spot 1.1000 over 6 months using the entered parity relationship.

Forward rate
1.110837
Forward points
0.010837
Forward premium / discount
0.99%
Annualized premium / discount
1.97%
Quote-currency rate
5%
Base-currency rate
3%
Implied forward rate The solved forward rate sits above spot, implying a forward premium for the base currency over this tenor.

Interpretation note

The solver shows the rate or forward level implied by the other inputs under covered interest parity. If real market quotes differ, the gap can reflect basis, funding, credit, collateral, or execution frictions rather than a clean arbitrage.

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FX Parity Solver

Forward rate calculator guide: solve the implied FX forward rate or one missing carry

A forward rate calculator solves the covered-interest-parity relationship between spot, tenor, and relative interest rates. It is useful when you want to estimate a forward FX rate from the carry differential or back out one missing rate from an observed spot and forward pair under a simplified parity assumption.

What the forward-rate solver is doing

The forward-rate solver treats spot, tenor, and the two currency rates as linked by a covered-interest-parity identity. If you know spot, tenor, and both rates, it solves the implied forward. If you know spot, forward, tenor, and one rate, it solves the missing rate that would make the relationship consistent.

That makes it useful for education, benchmarking, and quick sense checks. It is not intended to replace a real FX pricing engine or a dealer quote because practical forward markets also reflect basis, collateral, and execution details.

The formula and solve directions

The same parity identity can be rearranged several ways. This calculator keeps the quote convention fixed as quote currency per one base currency, then solves whichever variable you select from the remaining inputs.

When you solve for a rate, the output is an annual simple percentage over the entered tenor. When you solve for the forward rate, the tool also reports forward points and the implied premium or discount relative to spot.

Forward rate = Spot rate x (1 + Quote-currency rate x term) / (1 + Base-currency rate x term)

The covered-interest-parity identity used by the solver.

Quote-currency rate = (((Forward / Spot) x (1 + Base-currency rate x term)) - 1) / term

One rearrangement used when solving the quote-currency rate.

Worked example: solving the missing rate

Suppose spot is 1.1000, the observed six-month forward is 1.1108, and the base-currency annual rate is 3.00%. Solving the same relationship implies a quote-currency annual rate close to 5.00%.

You can reverse the same logic to solve the missing base-currency rate instead. The key point is that spot, forward, tenor, and carry inputs must fit together as one relationship when covered-interest-parity assumptions hold.

Why real markets can diverge from the solved output

Real FX forwards are not always equal to a frictionless parity estimate. Cross-currency basis, collateral terms, dealer balance-sheet costs, settlement conventions, and market stress can all push actual forward quotes away from the simple benchmark.

That does not make the solver useless. It makes it a baseline. A clean parity calculation helps isolate what the implied carry relationship would be before those other market frictions are layered on top.

Further reading

Frequently asked questions

What does this calculator solve for?

It can solve the implied forward FX rate, the quote-currency annual rate, or the base-currency annual rate from the other entered inputs under a simple covered-interest-parity assumption.

Why does the quote convention matter?

Because the parity formula depends on which currency is in the numerator and which is in the denominator. This calculator expects quote currency per one base currency, and changing that convention changes the interpretation of premium and discount.

Can real market forward quotes differ from the solved value?

Yes. Dealer spreads, basis, collateral, day-count conventions, and funding conditions can all move actual quotes away from a frictionless parity estimate.

Does this output guarantee an arbitrage opportunity?

No. A difference between market pricing and the solved value can come from practical market frictions rather than a clean, accessible arbitrage.

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