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solve-word-problems-involving-simple-interest-calculations

🚀 Simple interest is a way to calculate the interest charged or earned on a principal amount of money over a specific period of time. It is commonly used in banking and finance. The formula for calculating simple interest is: \[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \] where: - \( P \) is the principal amount (the initial amount of money), - \( R \) is the rate of interest per year, - \( T \) is the time in years. To solve word problems involving simple interest, we need to identify the principal, rate, and time from the problem statement and then apply the formula to find the interest or total amount.

Theory Explanation

Understanding the Components

In a simple interest problem, you need to identify three key components: the principal amount (P), the rate of interest (R), and the time period (T). The principal is the initial amount of money, the rate is usually given as a percentage, and the time is how long the money is invested or borrowed, typically in years.

Applying the Simple Interest Formula

Once you have identified P, R, and T, you can plug these values into the simple interest formula. Make sure to convert the rate from a percentage to a decimal if necessary, and ensure that the time is in years.

Calculating Total Amount

After calculating the simple interest, you can find the total amount of money after the interest is added to the principal. The total amount (A) can be calculated using the formula: \( A = P + SI \). This gives you the total amount after the interest has been applied.

Key Points

  • 🎯 Simple interest is calculated using the formula SI = (P * R * T) / 100.
  • 🎯 Identify the principal, rate, and time from the problem statement.
  • 🎯 The total amount after interest is A = P + SI.

Examples:💡

If you invest $1000 at a rate of 5% per year for 3 years, how much interest will you earn?

Solution:

Step 1: Identify the principal (P = 1000), rate (R = 5), and time (T = 3).

Step 2: Use the simple interest formula: SI = (P * R * T) / 100 = (1000 * 5 * 3) / 100 = 150.

Step 3: Calculate the total amount: A = P + SI = 1000 + 150 = 1150.

A loan of $2000 is taken at an interest rate of 6% per annum for 4 years. What is the total amount to be paid back?

Solution:

Step 1: Identify the principal (P = 2000), rate (R = 6), and time (T = 4).

Step 2: Calculate the simple interest: SI = (P * R * T) / 100 = (2000 * 6 * 4) / 100 = 480.

Step 3: Calculate the total amount to be paid back: A = P + SI = 2000 + 480 = 2480.

Common Mistakes

  • Mistake: Confusing the rate of interest with the total amount.

    Correction: Always remember that the rate is a percentage of the principal, not the total amount.

  • Mistake: Forgetting to convert the time into years if it is given in months or days.

    Correction: Make sure to convert all time periods into years before using the formula.

  • Mistake: Not adding the simple interest to the principal to find the total amount.

    Correction: Always remember to calculate the total amount by adding the simple interest to the principal.

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