Calculating the Simple Interest Rate on a Loan

Understanding Simple Interest

Simple interest is a method of calculating the amount of interest charged on a loan or earned on an investment. The formula for simple interest is I Prt, where I is the interest, P is the principal amount (the original loan amount), r is the interest rate, and t is the time period the loan is active in years.

Solving a Real-World Problem

A borrower pays a simple interest of $720 on a $3000 loan over a period of 2 years. To find the interest rate charged, we can use the simple interest formula and solve for r.

Using the Simple Interest Formula

The formula to find the interest rate when given the principal, time, and interest is:

r (100 * I) / (P * t)

Given:

Substitute the given values into the formula:

r (100 * 720) / (3000 * 2)

Calculate the result:

r (72000) / 6000

r 12

Therefore, the interest rate charged is 12%.

Alternate Methods to Solve the Problem

Another way to solve the problem is by breaking down the interest calculation for a single year and then adjusting for the total time period:

1. Interest for 2 years is $720, so for 1 year, the interest would be:

$720 / 2 $360

2. Now, finding the interest rate for the 1-year period:

Interest rate for 1 year (100 * 360) / 3000

Interest rate for 1 year 12%

Multiplying by the number of years (2) confirms the interest rate of 12%:

12% * 2 24% without considering compounding

Thus, the simple interest rate on the loan is 12%, indicating that the borrower is charged a 12% interest rate annually.

Using the Simple Interest Formula Directly

The direct application of the simple interest formula to find the rate is:

r I / (Pt)

Substitute the given values into the formula:

r 720 / (3000 * 2)

Calculate the result:

r 720 / 6000

r 0.12 or 12%

Therefore, the simple interest rate on the loan is 12%.

Conclusion

The problem involves calculating the simple interest rate for a given loan using the formula I Prt. By following the steps outlined, the interest rate can be accurately determined. The simple interest rate, in this case, is 12%, indicating that the borrower will be charged a 12% interest rate annually on the principal amount.