To calculate the repo rate on a repurchase agreement, divide the repurchase price by the purchase price, subtract 1, and multiply by 360 divided by the days to maturity. Written out: Repo Rate = [(Repurchase Price ÷ Purchase Price) − 1] × (360 ÷ Days to Maturity). Because U.S. repos use simple interest on an actual/360 basis, this one equation covers any term from overnight to several months. Overnight repo rates on Treasury collateral sat near 3.6% in mid-2026, closely tracking the Secured Overnight Financing Rate.1FRED, Federal Reserve Bank of St. Louis. Secured Overnight Financing Rate (SOFR)
The Four Inputs You Need
Before running the formula, gather four numbers. Any one of them wrong will move your annualized rate, sometimes by a lot.
- Purchase price: the cash the lender pays on the opening leg. This is the principal.
- Repurchase price: the cash the borrower pays to reclaim the securities on the closing leg. It equals the purchase price plus interest.
- Days to maturity: the actual calendar days between settlement of the first leg and settlement of the second. Overnight counts as one day.
- Day-count basis: U.S. repo uses actual/360, meaning actual calendar days over 360. Some non-U.S. markets use actual/365.2New York University Stern School of Business. The Repo Market
The day-count choice sounds like a technicality, but it isn’t. Using 365 instead of 360 on a large trade shaves basis points off the annualized rate, which on a $100 million position means real money. Confirm the convention in your Master Repurchase Agreement before plugging numbers in.
The Formula Step by Step
The annualized repo rate expresses the borrower’s cost as if the loan lasted a full year:
Repo Rate = [(Repurchase Price ÷ Purchase Price) − 1] × (360 ÷ Days to Maturity)
Broken into pieces, the logic is transparent. Dividing the repurchase price by the purchase price gives the total return ratio for the period. Subtracting 1 isolates the fractional gain, which is the un-annualized interest rate. Multiplying by (360 ÷ days) scales that fraction up to a full-year equivalent.
Worked Example
Say you lend $10,000,000 against Treasury notes for 30 days, and the agreed repurchase price is $10,030,000.
Step 1: $10,030,000 ÷ $10,000,000 = 1.003
Step 2: 1.003 − 1 = 0.003
Step 3: 0.003 × (360 ÷ 30) = 0.003 × 12 = 0.036, or 3.60%
That 3.60% is the annualized simple-interest rate. The word “simple” matters here: repos do not compound over the term. Even on a 90-day term repo, interest is a straight multiplication, not a compounded daily return. This convention keeps the math clean and matches how the broader U.S. money market quotes rates.
Solving for the Repurchase Price
In practice, dealers usually agree on a rate first and back out the repurchase price. Rearranged, the formula becomes:
Repurchase Price = Purchase Price × [1 + (Repo Rate × Days to Maturity ÷ 360)]
If you lend $50,000,000 for 14 days at 3.50%, the repurchase price is $50,000,000 × [1 + (0.035 × 14 ÷ 360)] = $50,000,000 × 1.001361 = $50,068,055.56. That $68,055.56 is the interest earned by the lender.
Converting the Rate to Dollar Interest
When the rate is already set and you want the dollar cost, the formula simplifies to:
Interest = Purchase Price × Repo Rate × (Days to Maturity ÷ 360)3Federal Reserve Bank of Richmond. Instruments of the Money Market – Repurchase and Reverse Repurchase Agreements
Take a $10,000,000 loan at 3.00% for 7 days. Interest is $10,000,000 × 0.03 × (7 ÷ 360) = $5,833.33. On a $1 billion overnight position, even a one-basis-point difference in the rate translates to roughly $277.78 per day, which is why Treasury desks watch fractions of a basis point.
Interest accrues on a straight-line basis over the term. The borrower books it as a financing cost; the lender records it as interest income.
How Haircuts and Initial Margin Change the Math
No lender hands over $100 million against exactly $100 million in collateral. The gap between the collateral’s market value and the cash lent is the lender’s cushion against a drop in collateral value before maturity. That gap changes the arithmetic you plug into the rate formula, because the purchase price is smaller than the securities backing it.
Haircut
A haircut is expressed as a percentage of the collateral’s market value:4International Capital Market Association. Frequently Asked Questions on Repo – What Is a Haircut
Haircut = (Market Value of Collateral − Purchase Price) ÷ Market Value of Collateral
If a borrower posts securities worth $100,000 and receives a $95,000 loan, the haircut is ($100,000 − $95,000) ÷ $100,000 = 5%. Treasury securities typically carry haircuts of 1–2%; lower-rated or less liquid bonds might require 5% or more.
Initial Margin
Initial margin expresses the same ratio from the collateral side:5International Capital Market Association. ICMA ERC Repo Margining Best Practices
Initial Margin = (Market Value of Collateral ÷ Purchase Price) × 100
In the same example, initial margin is ($100,000 ÷ $95,000) × 100 = 105.26%. A reading of 100% would mean no margin at all, so any figure above 100 shows how much overcollateralization the lender requires.
On a term repo, both sides mark the collateral to market. If its value falls enough that the lender’s exposure breaks the agreed margin, the lender issues a margin call for additional securities or cash. None of this changes the rate formula itself, but it changes what “purchase price” you use: the cash actually advanced, not the market value of the securities.
The Implied Repo Rate in Futures
If you trade bond futures, a related calculation comes up: the implied repo rate. It measures the theoretical return from buying a cash bond, selling a futures contract against it, and delivering the bond at expiration.
Implied Repo Rate = [(Futures Invoice Price − Cash Dirty Price) ÷ Cash Dirty Price] × (360 ÷ Days to Delivery)
The futures invoice price is the futures settlement price multiplied by the bond’s conversion factor, plus accrued interest at delivery. The implied repo rate tells arbitrageurs whether it is cheaper to fund a bond position in the repo market or synthetically through futures. When the implied repo rate exceeds the actual repo rate, there is a theoretical profit in buying the bond and selling the future, which is the classic basis trade.