Bond Accrued Interest
Computes the accrued interest of a fixed-income bond, the slice of coupon that has built up since the last coupon payment up to the settlement date. It uses the linear (actual-days) convention, proportional to elapsed days: interest = face value × (coupon rate ÷ frequency) × (days elapsed ÷ days in period). This is the amount the buyer pays the seller on top of the price, because the whole coupon goes to whoever holds the bond on the payment date. Enter the face value, the annual coupon rate, the number of coupons per year, the days since the last coupon and the days in the period.
Result
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Bond Accrued Interest
Computes the accrued interest of a fixed-income bond, the slice of coupon that has built up since the last coupon payment up to the settlement date. It uses the linear (actual-days) convention, proportional to elapsed days: interest = face value × (coupon rate ÷ frequency) × (days elapsed ÷ days in period). This is the amount the buyer pays the seller on top of the price, because the whole coupon goes to whoever holds the bond on the payment date. Enter the face value, the annual coupon rate, the number of coupons per year, the days since the last coupon and the days in the period.
The interest that ran up before you bought
Anyone who buys a bond partway between two coupons inherits a fairness problem: the whole coupon will land in the account of whoever holds the paper on the payment date, yet part of that interest was earned while the seller still owned it. Accrued interest sorts this out. It's the slice of coupon that has run up since the last payment, and the buyer hands it back to the seller at settlement.
The maths is proportional to time: take the period's coupon and multiply by the fraction of days already elapsed. A one-thousand bond with a 6% annual coupon paid twice a year earns 30 per half-year; if 90 of the 182 days in the period have passed, roughly half of those 30 already belong to the seller. It's an everyday calculation on a fixed-income desk, but it also shows up in exams and in the spreadsheets of anyone learning to price paper.
Enter the face value, the annual coupon rate, how many coupons the bond pays per year and the days (those already elapsed and those in the full period). The result is the cash amount to add to the price. Bear in mind there are several day-count conventions in the market; here we use the simple linear proportion, which is the most teachable and covers most practical cases.
Related Tools
Bond Dirty Price
Computes the dirty price of a bond: the clean price plus the interest accrued since the last coupon. The clean price is what shows up in quotes, but what actually changes hands at settlement is the dirty price, because the buyer has to reimburse the seller for the interest already run up. The tool works out the accrued interest on a linear basis and adds it to the clean price, returning both parts. Enter the clean price, the face value, the annual coupon rate, the coupon frequency, the days since the last coupon and the days in the period.
Bond Price from YTM
Computes the price of a coupon bond from its yield to maturity, discounting all future coupons and the face value to present: P = C·[1 − (1+i)^(−n)]/i + F·(1+i)^(−n). It's the inverse of computing the YTM and the foundation of fixed-income pricing. When the coupon exceeds the YTM, the bond trades at a premium; when below, at a discount. The calculation divides coupon and yield by the payment frequency. Enter the face value, the coupon rate, the YTM, the years and the coupons per year.
Z-spread (Zero-Volatility Spread)
Computes a bond's Z-spread: the constant spread added to the entire zero (spot) rate curve so the present value of its cashflows equals the market price. Unlike the nominal spread, which uses a single point, it accounts for the whole shape of the curve; for an option-free bond the Z-spread equals the OAS. Enter the cashflow times and amounts, the zero rate at each node and the price; the result is in basis points.
Interest Rate Caplet (Black Model)
Computes the premium of a caplet with the Black model: an option that pays when a period's interest rate exceeds a cap. A full interest rate cap is a sum of caplets, one for each payment period. It's the classic protection for someone who took a floating-rate loan and wants to limit how much they can pay. The price discounts the expected payoff to the payment date. Enter the forward rate, the cap rate, the volatility, the fixing time, the accrual fraction, the discount factor and the notional.
CIR Bond Price (Cox-Ingersoll-Ross)
Computes the price of a zero-coupon bond with the Cox-Ingersoll-Ross model, the successor to Vasicek that fixes its biggest flaw: CIR prevents negative interest rates, because the volatility shrinks as the rate approaches zero. It also has mean reversion and yields an affine closed form for the bond price. It's one of the most used short-rate models in practice. Enter the reversion speed, the long-run mean, the volatility, the current rate and the maturity.
Effective Convexity (Numerical)
Computes the effective convexity of a bond by finite differences, repricing the instrument for an up and a down yield move: (V− + V+ − 2·V0)/(V0·Δy²). Unlike analytical convexity, the effective version works even for bonds with uncertain cash flows, such as those with embedded options, because it only needs the three prices. It complements duration to better estimate the price change in large rate moves. Enter the three prices and the yield change used.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.