Monthly Savings Goal

How the monthly savings target formula works

For a target amount M, horizon of n months and monthly interest rate i (decimal), the required monthly contribution is PMT = M · i / ((1 + i)^n − 1). This is the future-value-of-annuity formula solved for PMT, and it assumes contributions are reinvested at the same rate. With no interest (i = 0), it degenerates to the trivial PMT = M / n.

Concrete example: to reach R$ 100,000 in 5 years (60 months) at a Selic-tracking rate of 1% per month, you need roughly R$ 1,224 per month. Without any yield, you would need R$ 1,667 per month — the compounding does R$ 443 of monthly heavy lifting for you. The gap widens dramatically as the horizon grows: over 20 years, compounding can cover more than half the target.

Common applications

Emergency fund (typically 6× monthly expenses), real-estate down payment (around 20% of property value), trips and sabbaticals, car replacement, exchange programs and tuition abroad, FIRE (Financial Independence Retire Early) targets, and university planning for children. Each scenario plugs different M and n values into the same equation.

FAQ

Which rate should I use? The net rate after tax of the product you actually invest in. Tesouro Selic and most CDBs follow a regressive income-tax table (22.5% to 15%); LCI/LCA and Tesouro IPCA in retirement-specific accounts are exempt.

Should I adjust the target for inflation? Yes — if the goal is far in the future, inflate M by expected IPCA or use a real (inflation-adjusted) rate instead of a nominal one to keep the result coherent.

What if I cannot afford the calculated PMT? Three levers: extend n, raise the rate by picking a higher-yield (still safe) product, or lower the target. Doubling the horizon usually cuts PMT by more than half thanks to compounding.