There are a lot of people that don’t need to use a calculator because they have jobs that don’t require a lot of math. However, there are people that have jobs where math is an everyday fixture. Not being able to do advanced math is something that will strongly work in your detriment if you […]

# Financial Mathematics

## How to Calculate Annualized Standard Deviation

A stock trader will generally have access to daily, weekly, monthly, or quarterly price data for a stock or a stock portfolio. Using this data he can calculate corresponding returns from the stock (daily, weekly, monthly, quarterly returns). He can use this data to calculate the standard deviation of the stock returns. The standard deviation […]

## Why Lognormal Distribution is Used to Describe Stock Prices

The concept of lognormal distribution is very closely related to the concept of normal distribution. Let’s say we have a random variable Y. This variable Y will have a lognormal distribution if the natural log of Y (ln Y) is normally distributed. So, we check if the natural logarithm of a random variable is normally […]

## Present Value of a Perpetuity

A perpetuity is a type of annuity that pays equal cash flows that occur periodically such as monthly, quarterly or annually for an infinite period of time. The present value of an annuity is calculated using the following formula: PV = A/r Where, A is the annuity payment, and r is the interest rate. Assume […]

## Future Value and Present Value of Ordinary Annuity

In an ordinary annuity, the first cash flow occurs at the end of the first period, and in an annuity due, the first cash flow occurs at the beginning (at time 0). The present value and future values of these annuities can be calculated using a simple formula or using the calculator. Future Value of […]

## Present Value of a Single Cash Flow

Present value of a single cash flow refers to how much a single cash flow in the future will be worth today. The present value is calculated by discounting the future cash flow for the given time period at a specified discount rate. The formula for calculating future value is: Example Calculate the present value […]

## Future Value of a Single Cash Flow

Future value of a single cash flow refers to how much a single cash flow today would grow to over a period of time if put in an investment that pays compound interest. The formula for calculating future value is: Example Calculate the future value (FV) of an investment of $500 for a period of […]

## Time Value of Money for Different Compounding Frequencies

Let’s first review the time value money concept using a very simple example. Example 1 Let’s say you have $2000 to invest. You decide to invest it for 3 years in an account that pays you an interest of 6% per annum. How much will your investment grow to in 3 years? We are calculating […]

## Interest Rate Equation

The required interest rate that an investor earns from an investment is made up of various components. The general interest rate equation is expressed below: The nominal risk-free rate itself is expressed as the sum of real-risk free rate and inflation premium. It is important to understand the difference between the nominal and real risk-free […]

## Types of Interest Rates

Interest rates are how we measure the time value of money. While making an investment, an investor will need to know the interest rate that the investment will earn. The interest rates can be interpreted in many ways. Required Rate of Return Required rate of return is the minimum return that an investor demands for […]