Video: Finding Growth Rate after a Certain Amount of Time in a Real-World Context

During a boom in the real estate market, the value of properties increased on average by 15% each year. What was the percentage increase every 5 years?

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Video Transcript

During a boom in the real estate market, the value of properties increased on average by 15 percent each year. What was the percentage increase every five years?

If we consider the original value to be 100 percent, then at the end of the first year following a 15 percent increase, the new value will be 115 percent. This means that our multiplier will be 1.15 per year. After two years, the multiplier would be 1.15 squared. In the same way, after three years, it would be 1.15 cubed. After four years, 1.15 to the power of four. And after five years, the multiplier would be 1.15 to the power of five.

As we’re asked for the percentage increase every five years. This is the value that we are interested in. The five-year increase will be equal to 1.15 to the power of five. 1.15 is equal to 2.01. Converting this to a percentage gives us 201 percent. Therefore, if the value of property is increased by 15 percent each year, there is approximately a 200 percent increase every five years.

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