Financial Mathematics Formulas: A Quick Guide

Financial mathematics is a crucial field for understanding and managing money, investments, and loans. It relies heavily on specific formulas to calculate present and future values, interest rates, and more. Here’s a breakdown of some essential formulas:

Simple Interest

Simple interest is the easiest way to calculate interest. It’s calculated only on the principal amount.

Formula: I = PRT

• I = Interest earned
• P = Principal amount
• R = Interest rate (per year, as a decimal)
• T = Time (in years)

Future Value (with Simple Interest): FV = P(1 + RT)

• FV = Future Value

Compound Interest

Compound interest is interest calculated on the principal and the accumulated interest from previous periods. It leads to much faster growth than simple interest.

Formula: FV = P(1 + i)^n

• FV = Future Value
• P = Principal amount
• i = Interest rate per compounding period (Annual rate / Number of compounding periods per year)
• n = Number of compounding periods (Number of years * Number of compounding periods per year)

Present Value

Present value calculates the current worth of a future sum of money, given a specified rate of return or discount rate. It essentially reverses the compounding process.

Formula (Compound Interest): PV = FV / (1 + i)^n

• PV = Present Value
• FV = Future Value
• i = Interest rate per compounding period
• n = Number of compounding periods

Annuities

An annuity is a series of equal payments made at regular intervals.

Future Value of an Ordinary Annuity: FV = PMT * [((1 + i)^n - 1) / i]

• FV = Future Value
• PMT = Payment amount per period
• i = Interest rate per period
• n = Number of periods

Present Value of an Ordinary Annuity: PV = PMT * [(1 - (1 + i)^-n) / i]

• PV = Present Value
• PMT = Payment amount per period
• i = Interest rate per period
• n = Number of periods

Amortization

Amortization is the process of paying off a debt over time through regular payments.

Loan Payment Formula: PMT = (PV * i) / (1 - (1 + i)^-n)

• PMT = Payment amount per period
• PV = Present Value (Loan Amount)
• i = Interest rate per period
• n = Number of periods

These formulas are the foundation of many financial calculations. Understanding them allows you to make informed decisions about saving, investing, and borrowing.