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Compound Interest

In: Economic Analysis Through Mathematics

Author

Listed:
  • Zrinka Lukač

    (University of Zagreb, Faculty of Economics & Business)

Abstract

Compound interest is the most widely used form of interest in business transactions. Here, the interest earned in one period also earns interest in the following period. Therefore, the speed of accumulation over time is much faster than that of simple interest. We start by deriving the fundamental compound interest formula, and then we discuss what to do if the interest conversion period does not coincide with the nominal interest rate. We show how to compute equivalent interest rate and effective interest rate. Next, we consider continuous compounding, that is, what happens if the number of interest conversion periods grows to infinity. One of the common problems in business practice is to find the principal P which accumulates to an amount S. Therefore, we consider discounted value, both for the case of discretely and continuously compounded interest. Then we show how to find the rate (given principal P, accumulated value S, and time n), as well as how to find time (given principal P, accumulated value S, and interest rate i). We conclude the chapter by showing how to compare cash flows due at different date, which leads us to the concept of equivalent amounts and equations of value.

Suggested Citation

  • Zrinka Lukač, 2026. "Compound Interest," Springer Texts in Business and Economics, in: Economic Analysis Through Mathematics, chapter 25, pages 553-585, Springer.
    • Handle: RePEc:spr:sptchp:978-3-032-08812-3_25
    DOI: 10.1007/978-3-032-08812-3_25
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