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Simple interest is a straightforward way to calculate the interest you earn or owe on a loan or an investment. It can be calculated using the simple interest formula: \[ I = P \times r \times t \] where:

• I is the interest
• P is the principal amount (the initial sum of money)
• r is the annual interest rate (as a decimal)
• t is the time the money is borrowed or invested for, in years

Before using the formula, ensure all units are standardized; for instance, convert the interest rate from a percentage to a decimal by dividing by 100, and convert time to years if it’s given in months or days. For the exercise above, Airin borrowed \( \$ 3900 \) at an interest rate of 4\% for 15 months. Convert the percentage to a decimal by dividing 4\% by 100, resulting in 0.04. Also, convert 15 months to years: \( \frac{15}{12} = 1.25 \) years. Plugging these values into the formula gives \[ I = 3900 \times 0.04 \times 1.25 \] which simplifies to: \[ 195. \] Airin owes \( \$ 195 \) in interest.

Calculating interest, especially simple interest, involves using a clear and consistent process. Here's a breakdown:

• Identify the Principal Amount: This is the starting amount of the loan or investment. In the exercise, this amount was \( \$ 3900 \).
• Determine the Annual Interest Rate: This is often provided in percentage form. Convert it to a decimal by dividing the percentage by 100. For a 4\% interest rate, this becomes 0.04.
• Convert Time to Years: Interest rates are usually annual, so time should be in years. For time periods given in months, divide by 12. Here, 15 months converts to \frac{15}{12} or 1.25 years.
• Apply the Simple Interest Formula: Plug the values into the formula \[ I = P \times r \times t \]. For Airin's case: \[ I = 3900 \times 0.04 \times 1.25 \] Do the arithmetic in steps: \[ 3900 \times 0.04 = 156 \] and \[ 156 \times 1.25 = 195 \].

By following these steps, you ensure consistency and correctness in your calculations.

When borrowing money, understanding loan repayment math is crucial. Simple interest calculations are often used for short-term loans to determine how much extra you will pay based on the interest rate and time. In the provided exercise, Airin borrowed \( \$ 3900 \) and promised to repay it in 15 months with a 4\% interest rate. The interest she owes, calculated using the simple interest formula, amounts to \( \$ 195 \).The total repayment amount is the sum of the principal and the interest. So, for Airin:\[ \text{Total Repayment} = \text{Principal} + \text{Interest} \]Plugging in the values,\[ \text{Total Repayment} = 3900 + 195 = 4095 \]. Airin will need to repay her parents \( \$ 4095 \).

• Principal + Interest = Total Repayment: This helps in knowing the total amount to be paid back. Good for budgeting and financial planning.
• Affordability: Before taking a loan, calculate if you can afford the total repayment.
• Short-term vs. Long-term: Simple interest is best for short-term loans. For long-term loans, compounded interest might be more relevant.

By understanding these fundamental calculations, you'll be better prepared to manage and repay loans effectively.