Mixed (Hamburg) Interest Calculator

Mixed interest: combining simple and compound

Mixed interest applies when a contract uses one regime for part of the term and another for the rest. The typical Brazilian convention: compound over the whole-month portion (n full months) and simple for the fractional remainder (f days, as a fraction of a month). The amount after a period of n + f months at rate i per month is M = C · (1 + i)n · (1 + i · f). Some contracts invert the order — simple first, compound afterward. Example: R$ 10,000 at 1% per month for 6 months and 15 days (n = 6, f = 0.5). Compound part: 10,000 · 1.01⁶ ≈ R$ 10,615.20. Simple part on the half-month: 10,615.20 · (1 + 0.005) ≈ R$ 10,668.28. Compare with pure compound (10,000 · 1.01^6.5 ≈ R$ 10,668.13): mixed yields slightly more because simple interest on the tail does not discount the fraction.

Applications: financing, leasing and judicial debt

Mixed interest shows up in Brazilian SFH mortgages, vehicle leasing, the Price table with fractional periods, and judicial debt updates — São Paulo's TJSP Tabela Prática is a classic example. Some banks bill broken months as simple interest, others use pro-rata-die compounding; always check the contract clause.

FAQ

Why use mixed instead of pure compound? Tradition and law: many older Brazilian financial standards specify simple interest for fractional periods, partly because it is easier to compute by hand and slightly favors the creditor.

Is mixed interest legal in consumer contracts? Brazil's STJ has accepted compound interest in bank contracts since 2000 (MP 2.170-36), but the exact handling of broken months depends on the clause and may be challenged.

Does the order matter (simple-then-compound vs compound-then-simple)? Slightly. Compound-then-simple gives a marginally higher amount because the simple portion compounds on a larger base.

How do I convert daily to monthly rate? Compound equivalence: i_monthly = (1 + i_daily)³⁰ − 1. Simple equivalence: i_monthly = 30 · i_daily.