Monthly Compound Interest Calculator

Monthly compound interest: M = C·(1+i)^t

With compound interest you put the earnings back to work each period, and the balance grows geometrically: M = C·(1+i)^t. Here C is the principal, i the monthly rate as a decimal and t the number of months. Take R$ 1,000 at 1 % a month over 12 months. That gives M = 1000·(1.01)^12 ≈ R$ 1,126.83, which beats the nominal 12 % (R$ 1,120). The gap comes from compounding every month, which pushes the effective annual rate to (1.01)^12 − 1 ≈ 12.68 %. When you need to move between rates, the formula is i_year = (1+i_month)^12 − 1. Brazilian products quoted by the month (CDB, LCI, LCA) tend to compound monthly. The Selic and most fixed income are quoted per year, yet the investor still sees the return accrue month by month.

Applications

Savings accounts (poupança), CDBs and LCIs, investment funds, Tesouro Direto (Selic, IPCA+, Prefixado), retirement planning (PGBL/VGBL), real estate financing (SAC/Price) and credit card revolving debt all lean on monthly compounding to project numbers that hold up.

FAQ

Simple vs compound interest? Simple is M = C·(1 + i·t); compound is M = C·(1+i)^t. The two agree at t = 1 period and then split apart, with compound coming out ahead for every t > 1.

Why is 12 % per year ≠ 1 % per month? When 12 % per year compounds monthly, the monthly figure works out to 0.9489 % (since (1.009489)^12 ≈ 1.12). Going the other way, 1 % per month adds up to 12.68 % per year. That extra slice is the compounding at work.

How is income tax (IR) applied? In Brazil, fixed-income IR runs on a regressive scale: 22.5 % up to 180 days, 20 % up to 360, 17.5 % up to 720 and 15 % beyond that. It hits only the earnings and is withheld when you redeem.