An investment grows by multiplying its value each period. A logarithm converts that growth into a rate and lets you add returns across consecutive periods. This lesson explains exponentials, logarithms and their allowed inputs. You will use them to calculate present value and prepare for differentiation.
Learning objectives. By the end of this note you should be able to:
- apply the laws of exponents and logarithms;
- move between exponential and logarithmic equations;
- compute future value, present value and a continuously compounded rate;
- explain why log-returns add through time;
- respect the domain restrictions of logarithms.
In this lesson
- Exponential growth and discounting
- Logarithms undo exponentials
- Why log-returns add
- A compact formula map
- Growth and discounting over time
Before you start
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