Mathematical Finance

UNIT II

Mathematics of the Time Value of Money

Introduction

1. Simple Interest

2. Bank Discount

3. Compound Interest

4. Annuities

Unit II Summary

List of Formulas

Exercises for Unit II

Introduction

The time value of money, a key theoretical concept and fundamental tool in finance, refers to the bidirectional nature of the value of money as it fluctuates up and down over time. Generally, in the absence of an interest rate, money tends to have a higher value in the present and a lower value in the future. Three factors may explain this fact: inflation, consumer impatience, and life uncertainty. Inflation is a steady rise in the general level of the price of goods and services. When these prices increase, the purchasing power of money decreases, simply because more money will be needed after inflation begins to make the same purchases as were made before. However, even if there is no inflation, certain noninflationary factors, such as consumer impatience and the uncertain nature of life, would still contribute to decrease the value of money in the future compared to its value at present. Consumer impatience refers to people’s general preference for today’s satisfaction over tomorrow’s. Almost anyone would prefer to purchase a favorite car or stereo set today as opposed to next year or next month. So the immediate utility derived from the goods and services purchased immediately gives the money its higher current value compared to a lower value at a later time, which would yield ...