GCSE Maths - How to Calculate Simple Interest

Summary

In this video, viewers are introduced to simple interest calculations, using relatable examples. The script explains how to calculate the interest on a loan or investment, starting with a 200-pound example at a 3% annual rate. It details how to compute interest for 1, 2, and even 10 years, and contrasts simple interest with more complex calculations for longer periods. The video then walks through an example involving a 600-pound investment at 2.1% interest over 6 years, demonstrating how to apply the formula to find the total amount. It concludes with a brief recap and invitation to like and subscribe.

Takeaways

• 😀 Simple interest is calculated by multiplying the principal amount by the interest rate and the time period.
• 😀 In simple interest, the interest is added each year based on the original amount, not compounded.
• 😀 To find the interest for one year, multiply the principal by the interest rate (in decimal form).
• 😀 Example: 3% interest on 200 pounds results in 6 pounds of interest each year.
• 😀 For multi-year loans, the interest for each year is added to the principal for the total amount owed.
• 😀 For a loan lasting multiple years, the interest for each year can be multiplied by the number of years to calculate total interest.
• 😀 Simple interest is easy to calculate for short-term loans (1–3 years), but for longer loans (e.g., 10 years), a different technique is used.
• 😀 Example for a 10-year loan: 200 pounds + (6 pounds per year * 10 years) = 260 pounds total.
• 😀 The same method applies when calculating the total amount of an investment with simple interest, such as Dora's 600 pounds in a 2.1% bank account.
• 😀 Dora’s investment of 600 pounds for 6 years at 2.1% simple interest results in a total of 675 pounds 60 pence at the end of the 6 years.

Q & A

What is simple interest?

Simple interest is a method of calculating the interest charged on a principal amount, where the interest is applied only to the original principal over the entire period of the loan or investment.

How do you calculate the interest on an amount?

To calculate interest, you multiply the principal amount by the interest rate (in decimal form) and the number of years. For example, 3% of 200 pounds for one year is calculated as 200 * 0.03 = 6 pounds.

What does the phrase '3 percent a year' mean in terms of simple interest?

It means that every year, the interest charged is 3% of the initial amount of money, not the accumulated total, which remains constant throughout the period.

What is the formula to find the total amount owed in simple interest?

The formula is: Total Amount = Principal + (Principal * Interest Rate * Time in Years). For example, for 200 pounds at 3% for 1 year, Total = 200 + (200 * 0.03 * 1) = 206 pounds.

Why do we divide the percentage by 100 when calculating simple interest?

We divide the percentage by 100 to convert the percentage into its decimal form, which allows for easier multiplication with the principal amount.

How do you calculate simple interest for multiple years?

For multiple years, you can simply multiply the interest per year by the number of years and then add it to the principal. For example, for 2 years, if the interest is 6 pounds per year, Total = 200 + (6 * 2) = 212 pounds.

What is the main difference in calculating simple interest for short and long periods?

For short periods (1-3 years), you can add the yearly interest for each year, while for long periods, you multiply the annual interest by the number of years and add it to the principal in one step.

How do you calculate the total after 10 years with a simple interest rate?

For 10 years, calculate the annual interest first (6 pounds in this case) and multiply it by 10, then add it to the principal. For example, 200 pounds + (6 pounds * 10) = 260 pounds.

How does Dora’s investment of 600 pounds with a 2.1% interest rate for 6 years work?

Dora’s annual interest is calculated as 600 * 0.021 = 12.60 pounds per year. Over 6 years, the total interest is 12.60 * 6 = 75.60 pounds. The total amount at the end of 6 years is 600 + 75.60 = 675.60 pounds.

What is the importance of converting percentages into decimals when calculating interest?

Converting percentages to decimals simplifies the calculation process. Percentages are based on 100, so dividing by 100 turns them into decimal form, making them easy to use in multiplication for calculating interest.