Compound Interest - Corbettmaths

Summary

This video provides a comprehensive guide to understanding compound interest through various examples. It covers both non-calculator and calculator-based methods, demonstrating how to apply percentages year by year. The video explains the essential compound interest formula and applies it to scenarios involving both growth and decay, such as bank investments and water tank leakage. Key examples include calculating compound interest for different rates and times, as well as solving problems with increasing and decreasing percentages. Viewers will gain a solid grasp of the concept and practical problem-solving techniques for compound interest.

Takeaways

• 😀 Compound interest is calculated using the formula: Initial Amount × (1 + Interest Rate) ^ Time.
• 😀 For non-calculator problems, you can manually apply the percentage increase year by year.
• 😀 For calculator-based problems, use the formula with the multiplier to simplify the process.
• 😀 In non-calculator problems, to find the amount after each year, calculate the interest and add it to the balance.
• 😀 For compound interest questions, the multiplier for a percentage increase is (1 + Interest Rate).
• 😀 For compound interest with a decrease, the multiplier is (1 - Interest Rate), as seen with the water tank example.
• 😀 In decreasing problems, like the water tank, you use a multiplier less than 1, e.g., 0.95 for a 5% decrease.
• 😀 Always round the final amount to two decimal places when dealing with money.
• 😀 In compound interest problems, if the question asks for a percentage decrease, subtract the remaining percentage from 100%.
• 😀 To find when a value exceeds a certain amount (e.g., tree growth), apply the formula and test different values for time.
• 😀 Showing your method and calculations step by step is crucial, especially for finding exact answers like when the tree exceeds 12 meters.

Q & A

What is the formula used for calculating compound interest?

The formula for compound interest is: Initial amount × (1 + interest rate) ^ time.

How does the non-calculator method for compound interest work?

In the non-calculator method, you calculate the percentage of the initial amount for each year, add it to the balance, and repeat the process for each time period (e.g., each year).

What was David’s investment in the first example, and how much interest did he earn after two years?

David invested £3,000 at 10% interest for two years. After two years, he earned £630 in interest, bringing his total balance to £3,630.

How does the calculator method for compound interest differ from the non-calculator method?

The calculator method uses the formula Initial × (1 + interest rate) ^ time, which allows for quicker and more efficient calculations compared to manually adding the interest each year as in the non-calculator method.

What multiplier is used when applying 3% interest in the second example?

The multiplier used for 3% interest is 1.03, which represents the 100% original amount plus 3% (i.e., 1 + 0.03).

What would Emily’s total balance be after four years if she invested £8,000 at 3% interest?

After four years, Emily would have £9,004.07 in the bank, which includes £1,004.07 in interest.

How is the compound interest formula applied to a situation with decreasing values, like the water tank example?

In the water tank example, the value decreases by 5% each hour. The formula is applied using a multiplier of 0.95 (100% - 5%) to calculate the remaining amount over time.

What percentage of water remains in the tank after three hours if it loses 5% per hour?

After three hours, 85.74% of the water remains in the tank.

In the tree height example, what was the tree’s initial height and how did it grow?

The tree’s initial height was 2 meters, and it grew by 30% per year. After 7 years, the tree’s height exceeded 12 meters.

Why is it important to show your work when solving compound interest problems on tests or homework?

Showing your work ensures that your method is clear and can help you track your calculations, making it easier to spot errors and demonstrate your understanding of the process.