Question

If your receive \(500 in simple interest on a loan that you made for \)10,000 for five years, what was the interest rate you charged?

Short answer

The interest rate charged was 1% per year.

Step-by-step solution

Write down the given information

We know that: Simple Interest = $500 Principal Amount (P) = $10,000 Time (T) = 5 years

Use the simple interest formula

According to the simple interest formula: Simple Interest = Principal x Rate x Time Plug in the given information and let R be the interest rate: \(500 = \)10,000 x R x 5

Solve for interest rate (R)

Now we need to solve for R: \(500 = \)10,000 x R x 5 Divide both sides by $10,000 to isolate R: \(\frac{500}{10000} = R \times 5\) Now, divide by 5: \(R = \frac{500}{10000 \times 5}\)

Simplify and find the interest rate

Simplify the fraction to find the interest rate: \(R = \frac{500}{50000}\) Now divide: \(R = 0.01\) Multiply by 100 to convert to a percentage: R = 1% The interest rate charged was 1% per year.

Key concepts

Simple Interest Formula

Understanding the simple interest formula is crucial for calculating the interest earned or paid on a loan or investment when the interest does not compound. The formula is represented as:

Simple Interest = Principal \times Rate \times Time

In the context of the given exercise, where a \(500 interest was received on a loan of \)10,000 over five years, the formula helps us find the unknown rate. The principal amount refers to the initial sum of money that was loaned out, the rate is the percentage of interest charged annually, and the time is the period for which the money is borrowed. By rearranging the formula, you can solve for any of the variables if the other two and the simple interest amount are known.

Interest Rate Calculation

The interest rate calculation involves finding the percentage of the principal that is paid as interest over a specific time period. In the example provided, with a principal amount of \(10,000 and an interest of \)500 gained over five years, we needed to determine the yearly interest rate. The formula for the rate R is given by:

R = \(\frac{\text{Simple Interest}}{\text{Principal} \times \text{Time}}\)

By inserting the known values into the formula, we calculated that the annual interest rate is 1%. It's worth noting that when expressing an interest rate, it's converted into a percentage to clearly communicate the proportion of the principal it represents – a crucial piece of information for financial planning and comparison.

Principal Amount

The principal amount in financial terms refers to the original sum of money borrowed or invested before any interest is added. It is the starting point for most financial calculations related to loans and investments. In the exercise example, the principal amount is $10,000, which is the initial loan amount. It's critical to accurately know the principal amount, as it directly affects the calculation of interest. When lending or borrowing money, always ensure that the principal amount is clearly defined and agreed upon, as any errors could result in incorrect interest computations or misunderstandings about the loan's or investment's terms.