Compute the implied forward interest rate from the spot curve, bootstrap inter-period forwards, and simulate Forward Rate Agreement (FRA) payoffs — all right in your browser.
The forward rate for period t1 → t2 locked in by today’s spot curve:
f(t1,t2) = [(1+r2)t2 / (1+r1)t1]1/(t2−t1) − 1
Enter a spot rate series, one line per curve point, in the format tenor_years,spot_percent. Tenors must increase.
An FRA payer locks in a borrowing rate (pay fixed, receive floating); a receiver does the opposite. The payoff is settled at the start of the period (discounted): Payoff = N × (L − K) × τ / (1 + L × τ), with τ = days/360.
A forward rate is the implied interest rate for a future period already locked in by today’s spot interest-rate curve. It answers: what interest rate is consistently implied by the market for a loan starting at t1 and ending at t2. Example: if the 1-year spot rate is 3% and the 2-year spot rate is 4%, the forward rate for year 2, f(1,2), is 5.0097% per year.
With discrete annual compounding, the formula is f(t1,t2) = [(1+r2)^t2 / (1+r1)^t1]^(1/(t2-t1)) - 1, where r1 and r2 are the spot rates at tenors t1 and t2. Example: r1 = 3%, t1 = 1 year, r2 = 4%, t2 = 2 years, then f(1,2) = (1.04^2 / 1.03) - 1 = 5.0097% per year.
No. A forward rate is an arbitrage-free number computed from the current spot curve, not a forecast. Pure expectations theory holds that the forward rate equals the market’s expectation of future rates, but other theories such as preferred habitat and the liquidity premium argue there is a term premium, so forward rates can be systematically higher or lower than expectations. Treating forward rates as forecasts is a common mistake.
Both use the word forward but their objects differ. An interest-rate forward rate is derived from the domestic spot curve and is quoted in percent per year for a borrowing period. An FX forward premium is the forward-minus-spot difference for a currency pair. The two are indeed linked through covered interest parity, but one measures the cost of funds across time while the other measures the price of currency across time.
Bootstrapping is the technique of deriving consecutive inter-period forward rates from the available spot rate series. The first period’s forward rate equals the shortest-tenor spot rate, then each subsequent period is computed from the two bracketing spot points. Example: 1-year spot 3%, 2-year 4%, and 3-year 4.5% give a 1-to-2-year forward of 5.0097% and a 2-to-3-year forward of 5.5072%.
A forward rate agreement is a contract that locks in a borrowing or deposit rate for a future period. The FRA payer pays the locked-in fixed rate and receives the realized reference rate, so it profits when the realized rate ends up above the locked-in forward rate. Example: notional Rp1,000,000, fixed 5%, realized rate 5.5%, 90-day period — the payer receives Rp 1,233.05 as the settlement value discounted to the start of the period.
Yes. If the spot curve is sufficiently negative, forward rates turn negative too, as happened with benchmark rates in Europe and Japan. Example: 1-year spot -1% and 3-year spot 0.5% give a 1-to-3-year forward of 1.2585%. The formula’s limits: tenor t2 must exceed t1, and no rate may be less than or equal to -100%.
Free tool by NRTechStudio
Explore similar finance tools and calculators. 100% free, accurate, and runs completely in your browser without sign-up.
2 taps, no typing needed — diagnostics are sent automatically.