Video Transcript
The population of a country was 22 million people at the end of 2010. Since then, the population has increased by 1.8 percent yearly. Determine the population of the country at the end of 2023. Give your answer in units of millions, correct to two decimal places.
Well, if we take a look at this question, we can actually see that it’s a compound interest question. And we know that because in the question, the population is increasing by 1.8 percent yearly. And that means that at the end of each year, another 1.8 percent is added on. So therefore, if it’s compound interest, we have a formula to help us. And that formula is that 𝐴 is equal to 𝑃 multiplied by one plus 𝑟 to the power of 𝑛, where 𝐴 is the amount. So it’s the amount that we’re looking for. 𝑃 is the principal, so that’s the initial amount. 𝑟 is the interest, and that’s the interest as a decimal. And our 𝑛 is the number of time periods. And in this case, that is actually years. Okay, great. So we now have our formula. And we now know the different parts. So let’s actually go on and solve the problem.
So first of all, we’re gonna make a note of the information we actually have. So we have that 𝑃 is equal to 22 because our principal amount was 22 million people. The reason I’ve kept it as 22 and haven’t written 22 and then million, is because actually we want the answer in units of millions. So we can actually leave it just as the 22. Next, we have 𝑟 which is equal to 0.018. And that’s because we increase by 1.8 percent yearly. Be careful with this because a common mistake here is actually 0.18. But remember, you have to actually divide your 1.8 by 100, which will give us 0.018. So then finally, we have 𝑛 which is the number of time periods, in this case, years.
So originally, the population was at the end of 2010, so 2010. And then, we’re looking for the population at the end of 2023 which is 2023. So therefore, 𝑛 is gonna be equal to 2023 minus 2010 which equals 13. Okay, great. We have all the information the question’s given us. So let’s get on and solve and find our amount. So we have 𝐴 is equal to 𝑃 multiplied by one plus 𝑟 to the power of 𝑛. So then, we substitute in our values. And we get 𝐴 is equal to 22 multiplied by 1.018 to the power of 13. And this gives us an answer of 27.7423. And then we need to carry out one more stage. Because it actually says, if we look back at the question, it wants the answer correct to two decimal places. So this gives us that 𝐴 is equal to 27.74.
So therefore, we can say that the population at the end of 2023 is 27.74 million, to two decimal places.
