Matemática Financeira: Desconto

In financial mathematics, discount (or “desconto” in Portuguese) refers to a reduction in the price of an asset, a product, or a financial instrument. It’s a fundamental concept used in various financial transactions, from everyday purchases to complex investment strategies. Understanding how discounts work is crucial for making informed financial decisions.

There are primarily two types of discounts: simple discount (desconto simples) and compound discount (desconto composto). The key difference lies in whether the discount is calculated only on the original principal (simple discount) or also on accrued discount (compound discount).

Simple Discount (Desconto Simples)

Simple discount is calculated only on the face value (nominal value) of the debt or instrument. The formula for simple discount is:

D = N * d * t

Where:

• D = Discount amount
• N = Nominal value (face value)
• d = Discount rate (per period)
• t = Time period (in the same unit as the discount rate)

The actual amount received, called the present value (valor atual) or discounted value, is calculated as:

PV = N - D

Simple discount is often used for short-term transactions, such as discounting checks or promissory notes. It’s conceptually simpler than compound discount, but it can be less accurate for longer periods.

Compound Discount (Desconto Composto)

Compound discount is similar to compound interest, but instead of adding interest to the principal, discount is subtracted. The formula for calculating the present value (PV) in compound discount is:

PV = N / (1 + i)^t

Where:

• PV = Present Value
• N = Nominal Value (face value)
• i = Interest rate (per period) – note this is effectively a “discount rate” applied in reverse
• t = Time period (in the same unit as the interest rate)

Unlike simple discount, compound discount takes into account the accumulated discount. This makes it more suitable for long-term financial transactions. The total discount (D) is calculated as:

D = N - PV

Rational Discount vs. Commercial Discount

Within simple discount, there are further distinctions between “rational discount” (desconto racional) and “commercial discount” (desconto comercial). Rational discount calculates the discount based on the present value, while commercial discount (also known as bank discount or simple interest discount) calculates the discount based on the future value. Commercial discount is more commonly used in banking practices, and it benefits the lender more than rational discount.

Applications of Discount

Discount concepts are used in various areas:

• Purchasing: Determining whether a discount offer is worthwhile.
• Finance: Evaluating investments based on their discounted cash flows.
• Banking: Calculating the effective interest rate on discounted notes.
• Accounting: Determining the present value of future liabilities.

Understanding the differences between simple and compound discount, as well as rational and commercial discount, is essential for anyone involved in financial transactions. These concepts provide tools for accurately evaluating the true cost or value of financial instruments and making informed decisions.

1024×768 matematica financeira desconto simples from www.slideshare.net