Financial Mathematics

The time value of money is a fundamental concept in Financial Mathematics, which recognizes that money today is worth more than the same amount of money in the future due to its potential earning power.

The formula for calculating the future value (FV) of a single sum is FV = PV * (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of compounding periods.

The formula for calculating the present value (PV) of a single sum is PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of compounding periods.

The formula for calculating the future value (FV) of an annuity is FV = PMT * [(1 + r)^n - 1] / r, where PMT is the periodic payment, r is the interest rate, and n is the number of compounding periods.

The formula for calculating the present value (PV) of an annuity is PV = PMT * [1 - (1 + r)^-n] / r, where PMT is the periodic payment, r is the interest rate, and n is the number of compounding periods.

The formula for calculating the internal rate of return (IRR) of an investment is IRR = (FV - PV) / PV, where FV is the future value, PV is the present value, and n is the number of compounding periods.

The formula for calculating the net present value (NPV) of an investment is NPV = FV - PV, where FV is the future value, PV is the present value, and n is the number of compounding periods.

The formula for calculating the payback period of an investment is Payback Period = Initial Investment / Annual Cash Flow, where Initial Investment is the initial cost of the investment, and Annual Cash Flow is the annual net cash flow generated by the investment.

The formula for calculating the breakeven point of an investment is Breakeven Point = Fixed Costs / (Selling Price - Variable Cost), where Fixed Costs are the fixed costs associated with the investment, Selling Price is the price at which the product or service is sold, and Variable Cost is the variable cost per unit sold.

The formula for calculating the Sharpe ratio of an investment is Sharpe Ratio = (Average Return - Risk-Free Rate) / Standard Deviation of Returns, where Average Return is the average return on the investment, Risk-Free Rate is the rate of return on a risk-free investment, and Standard Deviation of Returns is the standard deviation of the returns on the investment.

The formula for calculating the Treynor ratio of an investment is Treynor Ratio = (Average Return - Risk-Free Rate) / Beta, where Average Return is the average return on the investment, Risk-Free Rate is the rate of return on a risk-free investment, and Beta is the beta of the investment.

The formula for calculating the Jensen's alpha of an investment is Jensen's Alpha = Average Return - (Risk-Free Rate + Beta * Market Risk Premium), where Average Return is the average return on the investment, Risk-Free Rate is the rate of return on a risk-free investment, Beta is the beta of the investment, and Market Risk Premium is the difference between the expected return on the market portfolio and the risk-free rate.

The formula for calculating the information ratio of an investment is Information Ratio = (Average Return - Benchmark Return) / Standard Deviation of Excess Returns, where Average Return is the average return on the investment, Benchmark Return is the return on a benchmark portfolio, and Standard Deviation of Excess Returns is the standard deviation of the excess returns (investment return minus benchmark return).

The formula for calculating the Sortino ratio of an investment is Sortino Ratio = (Average Return - Minimum Acceptable Return) / Downside Risk, where Average Return is the average return on the investment, Minimum Acceptable Return is the minimum return that is considered acceptable, and Downside Risk is the standard deviation of the negative returns.