Tesouro Prefixado Unit Price (PU)
Computes Tesouro Prefixado unit price (PU) given rate and business days to maturity.
Preço unitário (PU): R$ —
Deságio: R$ —
Tesouro Prefixado: pricing zero-coupon Brazilian bonds (PU)
The PU (Preço Unitário) is the present value of a Brazilian government bond with a fixed nominal rate. For a zero-coupon prefixed bond (LTN), the formula is PU = VN / (1 + i)^(du/252), where VN is the face value at maturity (R$ 1,000.00 for LTN), i is the annual contracted rate, and du is the number of business days to maturity. Brazil uses 252 business days per year as the day-count convention — very different from the US 360/365 conventions.
There are two prefixed flavors on Tesouro Direto: LTN (Letra do Tesouro Nacional, zero-coupon — you buy at a discount and receive R$ 1,000 at maturity) and NTN-F (Nota do Tesouro Nacional – F, with semiannual 10% a.a. coupons plus principal at maturity). Both are marked-to-market daily: when market rates rise, PU falls, and vice-versa. If you hold to maturity you lock in the rate you bought at; if you sell early, you face interest-rate risk and may book a loss (or gain).
Applications
Use this PU calculation to verify Tesouro Direto quotes, plan target purchase prices, simulate portfolio mark-to-market in different rate scenarios, or estimate the discount you would receive on early redemption. Treasury desks, brokerages, and personal-finance spreadsheets all rely on this same formula. Liquidity is daily through B3, with the Treasury committing to buy back any holding.
FAQ
Why 252 instead of 365? Brazilian markets quote rates on a business-day basis, aligned with CDI and SELIC conventions. Holidays and weekends are excluded, so a year has roughly 252 trading days. Using 365 would understate the discount and give a wrong PU.
What happens if I sell before maturity? The Treasury buys back at the current market PU, which depends on prevailing rates. If rates rose since purchase, your PU fell — you may sell at a loss. If rates dropped, PU rose and you profit. Holding to maturity always delivers the agreed yield (gross of IR).
How is the income tax applied? Income tax on Tesouro Direto is regressive: 22.5% (up to 180 days), 20% (181–360), 17.5% (361–720), 15% (over 720 days), charged only on the gain at sale or maturity.
Related Tools
Treasury Prefixed Calculator (Brazil)
Simulate Treasury Prefixed: agreed annual rate, term to maturity. Applies regressive IR and shows redemption value.
Tesouro Prefixado Bond Yield Calculator
Computes gross yield of a Brazilian Tesouro Prefixado bond from invested amount, annual contracted rate and years to maturity.
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.
Prada Bag Price by Size
Estimates the approximate price of a Prada bag by size and model.
Bottega Veneta Cabat Bag Price
Estimates the approximate price of a Bottega Veneta Cabat bag by size.
Black-76 Put Price (Options on Futures)
Works out the premium of a European put option on futures with the Black-76 model, the Black-Scholes version for when the underlying is a future or forward contract. The price is e^(−rT)·[K·N(−d2) − F·N(−d1)], where d1 and d2 come from the futures price, the strike, the volatility and the term. The future already carries the cost of carry, so the discount factor multiplies both terms and interest does not enter d1. It applies to puts on commodities, indices and rates. Enter the futures price, the strike, the risk-free rate, the term in years and the annual volatility.
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.