What principle measures the increase in an amount of money as a result of interest earned?

The principle that measures the increase in an amount of money as a result of interest earned is the time value of money. This concept emphasizes that a sum of money has a greater value now than it will in the future due to its potential earning capacity. Essentially, money can earn interest, meaning that any amount of money is worth more the sooner it is received.

This principle underpins many financial decisions, including investment choices, savings strategies, and loan evaluations. It demonstrates how money can grow over time through interest accumulation, making it a crucial factor in personal finance and investment planning. Therefore, the correct answer is the time value of money, as it encapsulates the fundamental idea that money's value changes over time due to interest.