7 Financial mathematics Calculate the final sum, the initial sum, the time period and the interest rate for an investment. Calculate the Annual Equivalent Rate for part year investments and compare this with the nominal annual rate of return. Calculate the Net Present Value and Internal Rate of Return on an investment | 7 Financial mathematics Series time and investment Learning objectives After completing this chapter students should be able to Calculate the final sum the initial sum the time period and the interest rate for an investment. Calculate the Annual Equivalent Rate for part year investments and compare this with the nominal annual rate of return. Calculate the Net Present Value and Internal Rate of Return on an investment constructing relevant spreadsheets when required. Use the appropriate investment appraisal method to decide if an investment project is worthwhile. Find the sum of finite and infinite geometric series. Calculate the value of an annuity. Calculate monthly repayments and the APR for a loan. Apply appropriate mathematical methods to solve problems involving the growth and decline over discrete time periods of other economic variables including the depletion of natural resources. Discrete and continuous growth In economics we come across many variables that grow or decline over time. A sum of money invested in a deposit account will grow as interest accumulates on it. The amount of oil left in an oilfield will decline as production continues over the years. This chapter explains how mathematics can help answer certain problems concerned with these variables that change over time. The main area of application is finance including methods of appraising different forms of investment. Other applications include the management of natural resources where the implications of different depletion rates are analysed. The interest earned on money invested in a deposit account is normally paid at set regular intervals. Calculations of the return are therefore usually made with respect to specific time intervals. For example Figure a shows the amount of money in a deposit account at any given moment in time assuming an initial deposit of 1 000 and interest credited at the end of each year at a rate of 10 . There is not a continuous relationship between time .
