Compound Interest - Corbettmaths

The video introduces compound interest and a crucial formula: 'initial multiplied by the multiplier to the power of time.' It also suggests repeatedly applying the percentage for non-calculator problems.

David invests £3,000 at 10% compound interest per year for two years. The solution involves calculating 10% of the principal for the first year, adding it on, and then calculating 10% of the new total for the second year. After two years, David has £3,630.

Emily invests £8,000 at 3% compound interest for four years. The formula 'initial x multiplier^time' is used. The initial amount is £8,000, the multiplier for a 3% increase is 1.03, and the time is 4 years. The calculation is 8000 * (1.03)^4, resulting in £9004.07 after rounding to two decimal places.

This example involves a water tank losing 5% of its water every hour for three hours. Since it's a percentage question, the initial amount is considered 100%. The multiplier for a 5% decrease is 0.95. The calculation is 100 * (0.95)^3, showing that 85.7375% of the water will be left.

A tree, initially 2 meters tall, grows by 30% per year. The goal is to find out how many years it takes for the tree to exceed 12 meters. The formula is 2 * (1.3)^time. The video demonstrates trying different 'time' values (5, 6, and 7 years) until the height exceeds 12 meters. After 7 years, the tree's height is 12.5497 meters, exceeding the target.

The video concludes by reiterating the importance of the formula 'initial times the multiplier to the power of time' for calculator questions and the method of repeatedly applying percentages for non-calculator compound interest problems, adjusting for increases or decreases.