Actuarial calculations in life insurance and pensions, Fundamentals...

Actuarial calculations in life and pension insurance

Yes, man is mortal, but it would not be so bad.

The bad thing is that sometimes it's suddenly dead, that's the focus!

Mikhail Bulgakov

Master and Margarita

Fundamentals of Financial Mathematics

As a result of the study of Chapter 6, the student must:


• The theoretical principles underlying the financial analysis;

• the main concepts and categories used in the practice of financial calculations;

• methods for evaluating the final results of financial transactions for each of the parties involved;

• types and characteristics of financial rent;

• Basics of quantitative analysis of payment sequences;

be able to

• evaluate the parameters, make calculations and analyze investment, credit and commercial transactions;

• Establish an equivalent link between the main financial indicators: effective and nominal interest and discount rates, discount rates and interest rates;

• determine the advance interest income, the present value of cash at any point in time;

• Evaluate the series of payments, determine the generalizing characteristics of the rent and their individual parameters, calculate the present value of deterministic, increasing and decreasing financial rents of any duration and frequency;

• compare the effectiveness of financial transactions;

• identify the dependence of the final settlement results on the main parameters of the contract;


• the basics of financial mathematics;

• principles of accretion, discounting of payments and accounting by simple and compound interest formulas;

• a calculation technique developed for the analysis of various types of financial rents;

• Methods of modern practice of performing financial calculations.

Basic concepts and financial indicators

In financial computing, the time factor is necessarily taken into account as one of the most important elements. The need to take into account the time factor is determined by the principle of disparity money related to different points in time. Inequality is determined by the fact that, theoretically, any amount of money can be invested and generate revenue, and the income received, in turn, can be reinvested.

An obvious consequence of the principle of "disparity is the illegality of the summation of monetary values ​​relating to different points in time. Such a summation is permissible only where the time factor does not matter - for example, in accounting for obtaining totals by periods and in financial control.

The accounting of the time factor in financial calculations is carried out by means of accrual of interest. Under interest (interest money) is understood as the absolute amount of income from providing money in debt in any form: in the form of issuing a monetary loan, selling on credit, when depositing money into a savings account, account of a bill, purchase of a savings certificate or bonds, etc.

When concluding a financial or credit agreement, the parties (the creditor and the borrower) agree on the amount of interest rate - the ratio of the amount of interest money paid out over a fixed period of time to the loan amount. The time interval to which the interest rate relates is called the charge period. The rate is measured in percent, as a decimal or natural fraction.

Interest calculation, as a rule, is carried out discretely, i.e. (usually equidistant) moments of time - discrete percentages. At the same time as the charging periods take a year, half a year, a quarter, a month. Sometimes, daily accrual is practiced, and in some cases it is convenient to apply continuous interest. Interest is either paid to the lender as they are accrued or added to the amount of debt.

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