Question

What is the total amount of interest from a $5,000 loan after three years with a simple interest rate of 6%?

Short answer

The total amount of interest from the $5,000 loan after three years with a simple interest rate of 6% is $900.

Step-by-step solution

Convert the interest rate to a decimal

To convert the percentage interest rate to a decimal, divide the rate by 100. In this case, we have 6%: \(Rate = \frac{6}{100} = 0.06\)

Calculate the interest

Now, plug the numbers into the interest formula: Interest = Principal × Rate × Time Interest = \(5,000 × 0.06 × 3\)

Perform the calculation

Multiply the numbers together: Interest = \(5,000 × 0.06 × 3 = 300 × 3 = 900\)

State the answer

The total amount of interest from the \(5,000 loan after three years with a simple interest rate of 6% is \)900.

Key concepts

Interest Rate Conversion

Understanding how to manipulate interest rates is essential in various financial calculations. When you encounter an interest rate, it's usually expressed as a percentage. However, to perform calculations, we often need to convert this percentage into a decimal form.

This process is simple and straightforward. To convert a percentage to a decimal, we divide the given percentage by 100. For instance, if we have an interest rate of 6%, the decimal form would be calculated as follows: \[\begin{equation} Rate = \frac{6}{100} = 0.06 \end{equation}\]

This is a crucial step because the interest calculation formulas require the rate to be in decimal form.

Simple Interest Formula

The simple interest formula is a fundamental concept in finance that enables you to calculate the interest earned or paid on a principal amount over a certain period. The basic formula for calculating simple interest is: \[\begin{equation} Interest = Principal \times Rate \times Time \end{equation}\]

Here, 'Principal' refers to the original sum borrowed or invested, 'Rate' is the interest rate in decimal form, and 'Time' represents the period of the loan or investment. Unlike compound interest, simple interest is calculated only on the principal amount and does not include interest on interest.

For example, using a principal of \$5,000, a rate of 6%, and a time duration of 3 years, the interest would be:\[\begin{equation} Interest = 5,000 \times 0.06 \times 3 \end{equation}\]

The simplicity of this formula lies in its straightforward calculation, which particularly suits short-term loans or investments.

Mathematical Calculations in Economics

Mathematics plays a pivotal role in economics by providing tools to model and analyze financial situations. Mathematical calculations enable economists and finance professionals to predict trends, assess interest, and make informed decisions on lending, borrowing, or investing.

Economic theories often rely on mathematical models to illustrate concepts such as inflation, supply and demand, and market equilibrium. Calculations such as the simple interest formula are just the tip of the iceberg, but they are crucial for building a strong foundational understanding of how money grows over time and how debts can accrue.

By grasping these calculations, students not only tackle academic exercises but also prepare themselves for real-world financial management. Being keen on precision and clarity when performing these calculations will result in a more accurate representation of economic scenarios.