Final answer:
Interest earned can be calculated using simple interest or compound interest methods. Simple interest applies the rate to the principal only, while compound interest applies the rate to the principal plus accumulated interest over time. Examples highlighting the differences in interest calculation methods help showcase the concept.
Step-by-step explanation:
The amount of interest earned from the force of interest can be understood through examples of simple interest and compound interest calculations. Simple interest is a straightforward calculation where the interest rate is applied only to the principal amount. For instance, an amount of $100 with a simple interest rate of 5% over three years would result in total interest earned of $15, making the future total amount $115. This is calculated as $100 + ($100 × 0.05 × 3).
On the other hand, compound interest is calculated on the principal plus the accumulated interest over time. As an example, if $100 is deposited in a bank account that has a 2% annual compound interest, the future total after one year would be $102. Continuing this calculation over three years would yield a total of $106.18, which is the result of $100 times 1.02³.
When considering loans or investments, these interest calculations determine the overall profitability or cost associated with them. For example, the total interest from a $5,000 loan at a simple interest rate of 6% over three years would amount to $900, calculated as $5,000 × 0.06 × 3.