Calculating the Yearly Rate of Interest for a Loan with Simple Interest

Mr. Mondragon borrowed PHP 30,000 from a bank. At the end of 6 months, he paid back PHP 30,750. To find the yearly rate of interest, we can use the formula for simple interest: Interest Principal × Rate × Time.

Understanding Simple Interest

Simple interest is a method to calculate the interest amount for a given principal over a specified period. The formula for simple interest is:

Interest Principal × Rate × Time

How to Calculate the Yearly Rate of Interest

To determine the yearly rate of interest, follow these steps:

Calculate the Interest Paid: The total interest paid is the difference between the total amount paid back and the principal amount borrowed. Rearrange the Formula: Rearrange the simple interest formula to solve for the rate. Solve for the Rate: Calculate the rate in decimal form and then convert it to a percentage. Convert to Yearly Percentage: Convert the rate to a yearly percentage by multiplying by 100.

Steps to Calculate the Yearly Rate of Interest

Step 1: Calculate the Interest Paid

In this example, Mr. Mondragon borrowed PHP 30,000 and paid back PHP 30,750 after 6 months. The interest paid can be calculated as follows:

Interest Total Amount Paid Back - Principal

Interest PHP 30,750 - PHP 30,000 PHP 750

Step 2: Rearrange the Formula to Find the Rate

Using the simple interest formula: Interest Principal × Rate × Time, we can rearrange it to isolate the rate:

750 30,000 × Rate × 0.5

Step 3: Solve for Rate

Rearrange the equation to solve for the rate:

750 15,000 × Rate

Rate 750 / 15,000 0.05

Step 4: Convert the Rate to a Yearly Percentage

To convert the rate to a yearly percentage, multiply by 100:

Rate of Interest 0.05 × 100 5%

Conclusion

The Yearly Rate of Interest

The yearly rate of interest for Mr. Mondragon's loan is 5%. This calculation assumes simple interest, where the interest is not compounded.

Alternative Method

If you want to calculate the annual interest amount based on the 6-month interest, you can multiply the 6-month interest by 2 to get the annual interest amount:

Annual Interest 750 × 2 PHP 1,500

Then, divide the annual interest amount by the principal sum:

Rate of Interest 1,500 / 30,000 × 100 5%

Additional Considerations

The calculation above assumes simple interest, but if the interest is compounded, the formula and process would be different. For compounded interest, you would use the formula for compound interest:

A P(1 r/n) ^ nt

where:

A the future value of the investment/loan, including interest P the principal investment amount (the initial deposit or loan amount) r the annual interest rate (decimal) n the number of times that interest is compounded per year t the number of years the money is invested or borrowed for

Tools and Calculators

For those who prefer using a calculator, you can use the HP 12C or a similar financial calculator. Alternatively, you can use online tools or software like Excel to perform these calculations more easily.

Conclusion

By following the steps outlined in this article, you can easily calculate the yearly rate of interest for a loan with simple interest. Whether you're a student, a lender, or a personal finance enthusiast, understanding how to calculate interest rates is a valuable skill.