Calculation Methodology and Formulas

Transparency is the foundation of Investmony. We detail below the premises, mathematical formulas, and regulatory bases used in each of our tools.

1. CDB and Fixed Income Simulator

Monthly Interest Capitalization

The simulations use the continuous or monthly compound interest regime. To calculate the final value before taxes, we add the monthly contribution $Vm$ to the initial balance and apply the effective monthly rate:

Balance_{t} = (Balance_{t-1} + $Vm$) \times (1 + $i_{monthly}$)

Annual Rate Equivalence to Monthly

Brazilian rates are expressed in annual terms. We convert nominal annual rates ($i_{annual}$) to effective monthly rates ($i_{monthly}$) using the classic equivalence formula:

$i_{monthly}$ = (1 + $i_{annual}$)^{1/12} - 1

Tax Rules (Regressive Table)

For taxable assets (CDB, Treasury Selic, Treasury IPCA, and Fixed-Rate Bonds), we apply the regressive Income Tax (IR) solely to the net profit (profit = final gross balance - total contribution):

• Up to 6 months (180 days): 22.5%
• From 6 to 12 months (181 to 360 days): 20%
• From 12 to 24 months (361 to 720 days): 17.5%
• Above 24 months (721 days or more): 15%

Real Estate and Agribusiness Credit Notes (LCI and LCA) receive a 0% tax rate (full tax exemption for individuals).

2. Financing Calculator (SAC vs PRICE)

Constant Amortization System (SAC)

The basic debt amortization ($A$) is linear and fixed every month:

$A$ = $\frac{\text{Financed Value}}{N_{\text{months}}}$

The interest ($J$) for each month charges the monthly rate on the remaining debt balance:

$J_t$ = $\text{Debt Balance}_{t-1}$ $\times$ $i_{monthly}$

The final monthly installment $t$ is the sum: $P_t$ = $A$ + $J_t$ + $\text{Insurance/Fees}$.

PRICE Table

The total monthly installment ($PMT$) before insurance is constant every month and calculated using the French amortization formula:

$PMT$ = $\text{Financed Value}$ $\times$ $\frac{i \times (1 + i)^N}{(1 + i)^N - 1}$

The amortization for each month varies and is calculated by deducting the charged interest: $A_t$ = $PMT$ - $J_t$.

Extra Amortization Mechanism

When the user makes an extra amortization, the debt balance is immediately deducted in the month of contribution. - **Reduce Term:** The bank maintains the base amortization or the $PMT$ and recalculates only the total term, which is reduced. - **Reduce Installment:** The bank maintains the final term and recalculates the periodic amortization (in SAC) or the $PMT$ installment (in PRICE) by dividing the remaining debt balance by the remaining term.

3. Retirement Planner

Fisher Equation (Real Return)

We discount the estimated inflation to work in terms of Real Purchasing Power (today's values), avoiding nominal illusions:

1 + $i_{real}$ = $\frac{1 + i_{nominal}}{1 + i_{inflation}}$

4% Rule (Safe Withdrawal)

We define the necessary wealth for financial independence by applying the annual safe withdrawal rate chosen by the user ($SWR$):

$\text{Target wealth}$ = $\frac{\text{Desired Annual Expense}}{\text{SWR Rate}}$