Part 2 book “Essential mathematics for economic analysis” has contents: Topics in financial mathematics, functions of many variables, tools for comparative statics, multivariable optimization, determinants and inverse matrices, matrix and vector algebra, linear programming, constrained optimization. | k 10 TOPICS IN FINANCIAL MATHEMATICS I can calculate the motions of heavenly bodies, but not the madness of people. —Isaac Newton1 T k his chapter treats some basic topics in the mathematics of finance. The main concern is how the values of investments and loans at different times are affected by interest rates. Sections and have already discussed some elementary calculations involving interest rates. This chapter goes a step further and considers different interest periods. It also discusses in turn effective rates of interest, continuously compounded interest, present values of future claims, annuities, mortgages, and the internal rate of return on investment projects. The calculations involve the summation formula for geometric series, which we therefore derive. In the last section we give a brief introduction to difference equations. Interest Periods and Effective Rates In advertisements that offer bank loans or savings accounts, interest is usually quoted as an annual rate, also called a nominal rate, even if the actual interest period is different. This interest period is the time that elapses between successive dates when interest is added to the account. For some bank accounts the interest period is one year, but it has become increasingly common for financial institutions to offer other interest schemes. For instance, many US banks used to add interest daily, some others at least monthly. If a bank offers 9% 1 × 9% = of the annual rate of interest with interest payments each month, then 12 capital accrues at the end of each month. The annual rate must be divided by the number of interest periods to get the periodic rate—that is, the interest per period. Suppose a principal (or capital) of S0 yields interest at the rate p% per period, for example one year. As explained in Section , after t periods it will have increased to the amount S(t) = S0 (1 + r)t , where r = p/100, which is p%. Each period the principal .
