Libor Rate Calculator

Use the calculator to (1) compute interest accrual and ending balance for a loan indexed to LIBOR or SOFR given a quoted rate, spread, principal, and dates.

• All Business Calculators
• Risk Premium Calculator
• Risk-Adjusted Return Calculator

LIBOR/SOFR Accrual and Related Formulas

The calculator above uses standard money-market style relationships for accrual, discount factors, and forward rates. (It does not reproduce the official LIBOR fixing methodology.)

\begin{aligned}
r_{\text{all-in}} &= r_{\text{quoted}} + \frac{\text{spread}_{\text{bps}}}{10{,}000} \\
t &= \frac{\text{Days}}{\text{Base}},\ \ \text{Base}\in\{360,365\} \\
I_{\text{simple}} &= P \, r_{\text{all-in}} \, t \\
I_{\text{comp}} &= P\left(\left(1+\frac{r_{\text{all-in}}}{m}\right)^{m t}-1\right) \\
DF &= \frac{1}{1+r t} \\
f_{t_1,t_2} &= \frac{DF(t_1)/DF(t_2)-1}{t_2-t_1} \\
r_{\text{LIBOR}} &\approx r_{\text{SOFR}} + \text{spread},\quad
r_{\text{SOFR}} \approx r_{\text{LIBOR}} - \text{spread}
\end{aligned}

Variables:

• P is the principal (dollars)
• r_quoted is the quoted benchmark rate as a decimal (e.g., 5% = 0.05)
• spread_bps is the added spread in basis points (1 bp = 0.01%)
• r_all-in is the all-in rate as a decimal (quoted rate plus spread)
• Days is the number of days between the start date and end date
• Base is 360 for ACT/360 or 365 for ACT/365 (day-count denominator)
• t is the year fraction (decimal)
• m is the compounding frequency per year (12 monthly, 4 quarterly, 2 semiannual, 1 annual)
• I is interest accrued (dollars)
• DF is the discount factor (simple money-market convention)
• f is the (simple) forward rate between t₁ and t₂
• spread (in the conversion line) is the fixed spread used to estimate an equivalent rate; the built-in “ISDA Fallback Spreads” are the fixed USD LIBOR fallback spreads by tenor

To compute accrued interest, first convert the quoted rate and any spread into an all-in rate, compute the year fraction from the day-count convention, and then apply either simple interest or the selected compounding convention.

What is a Libor Rate?

LIBOR (the London Interbank Offered Rate) was a set of benchmark interest rates intended to reflect the unsecured wholesale funding costs of large banks for specific currencies and tenors. It was produced from panel bank submissions and published by ICE Benchmark Administration (IBA). Most LIBOR settings ceased at the end of 2021, and the remaining widely used USD LIBOR settings ceased after June 30, 2023; some “synthetic” LIBOR settings have been published for limited periods for certain legacy contracts, depending on currency/tenor and regulatory decisions. In new contracts, LIBOR has largely been replaced by near risk-free reference rates such as SOFR (for USD).

How to Calculate Using a LIBOR or SOFR Rate?

The following steps outline how to calculate interest using a quoted LIBOR (or SOFR-based) rate and an added spread:

1. Enter the quoted rate (in %) and any added spread (in bps).
2. Enter the principal amount, choose a day-count basis (ACT/360 or ACT/365), and provide the start and end dates (or use the “Days” output).
3. Select simple interest or a compounding frequency, then calculate the year fraction and interest accrued.
4. Optionally, use the LIBOR ↔ SOFR tab to estimate an equivalent rate by adding/subtracting a fixed spread, or use the Discount/Forward tab for simple discount factors and forward rates.

Example Problem:

Use the following values as an example to test your knowledge (simple interest, ACT/360):

Quoted Rate = 5.00%

Added Spread = 20 bps (0.20%)