# The concept and tools for assessing the value of money over time

Financial management requires the constant implementation of various calculations related to cash flows in different periods of time. The key role in these calculations is played by the time value of money. Its essence is that the value of money changes over time taking into account the rate of return in the financial market. The same amount of money in different periods of time has a different value; this cost is now always higher than in any future period.

Financial management requires constant implementation of various financial and economic calculations related to cash flows in different periods of time. The key role in these calculations is played by the time value of money.

The concept of the value of money over time is that the value of money changes over time taking into account the rate of return in the financial market, which is usually the rate of loan interest (or interest). In other words, in accordance with this concept, the same amount of money in different periods of time has a different value; this cost is now always higher than in any future period.

The concept of the value of money over time plays a fundamental role in the practice of financial computing. It predetermines the need to take into account the time factor in the process of carrying out any long-term financial transactions by evaluating and comparing the cost of money at the beginning of financing with the cost of money when they are returned in the form of future profit, depreciation, the main amount of debt, etc.

In the process of comparing the value of cash when planning its flows over an extended period of time, two main concepts are used – the future value of money or their present value.

The future value of money is the amount of funds currently invested that they will turn into after a certain period of time, taking into account a certain interest rate (interest rate). The determination of the future value of money characterizes the process of increasing their value (compounding), which consists in joining the accrued interest amount to their initial amount.

The present value of money represents the amount of future cash, adjusted for a specific interest rate for the current time period. The determination of the present value of money characterizes the process of discounting their value, which represents the operation that is the inverse of the increase, carried out by removing from the future value the corresponding amount of interest (discount amount or “discount”).

When conducting financial calculations related to assessing the value of money over time, the processes of increasing or discounting the value can be carried out both at simple and complex interest.

Simple interest represents the amount of income accrued to the main amount of money capital in each interval of the total period of its use, for which its further recalculations are not carried out. The accrual of simple interest is applied, as a rule, in short-term financial transactions.

Compound interest is the amount of income accrued in each interval of the total period of its use, which is not paid, but is added to the main amount of the money interval and in the subsequent payment interval it generates income. Compound interest is applied, as a rule, in long-term financial transactions (investment, lending, etc.)

Calculations of the amount of interest can be carried out both at the beginning and at the end of each interval of the total time period. In accordance with this, the methods of calculating interest are divided into preliminary and subsequent.

A preliminary method of calculating interest (prenumerando method or antisipative method) characterizes the method of calculating payments, in which interest is calculated at the beginning of each interval.

The subsequent method of calculating interest (the postnumerando method or the recursive method) characterizes the method of payment in which interest is calculated at the end of each interval.

Payments related to the payment of the amount of interest and repayment of the principal amount of the debt are one of the types of cash flow, divided into discrete and continuous.

Discrete cash flow characterizes the flow of payments on invested cash capital, which has a clearly determined interest calculation period and a deadline for the return of its principal amount.

Continuous cash flow characterizes the flow of payments on invested cash capital, the interest calculation period for which is not limited, and accordingly, the deadline for the return of its principal amount is not defined. One of the most common types of continuous cash flow is annuity (financial annuity) – a long-term stream of payments characterized by the same level of interest rates in each of the intervals of the considered time period.