Financial Mathematics: Essential Concepts and Definitions

Financial Mathematics

Core Definitions

• Annuity: A series of equal payments made at regular intervals to pay off a debt or build a fund.
• Capital: The principal amount of money agreed upon for an investment or loan.
• Interest: The amount earned or paid for the use of money, directly proportional to capital, time, and the interest rate.
• Compound Interest: Interest calculated on the initial principal and also on the accumulated interest of previous periods; its growth is exponential.
• Simple Interest: Interest calculated only on the initial principal; the capital remains constant each period, resulting in arithmetic growth.
• Amount: The total sum of money to be paid or received at the end of an agreed period, calculated as capital plus interest.
• Deadline: The total number of periods for an investment.

Mathematical Progressions

• Arithmetic Progression: A sequence where the difference between consecutive terms is constant (the common difference). Example: 3, 6, 9, 12, 15 (ratio is 3).
• Geometric Progression: A sequence where each term is obtained by multiplying the previous term by a constant ratio. Example: 2, 4, 8, 16, 32, 64 (ratio is 2).
• Reason: The proportional relationship existing between two numbers.

Interest Rate Classifications

• Interest Rate: A fixed percentage of capital paid for the use of money. From a debtor's perspective, it is a cost; from an investor's perspective, it is a return.
• Effective Interest Rate: The actual interest rate that applies during each capitalization period.
• Equivalent Interest Rates: Different interest rates that yield the same financial results under varying conditions.
• Nominal Interest Rates: Rates referenced annually with m capitalization periods, which typically result in a higher effective rate.

Time Value of Money

The value of money is a function of time, directly proportional to the interest rate and duration.

Present Value

The current value of a future sum or stream of payments (annuity), discounted at a specific interest rate. It represents the equivalent value of future money in today's terms. For annuities, it is the capital required today to achieve a specific future amount based on an agreed interest rate.