Video Transcript
Daniel and Ethan work at two different companies. Daniel is paid 28,000 pounds in the first year and gets a three percent pay increase each year. Ethan is paid 30,000 pound in the first year and gets an increase of 1,250 every two years. Who is paid the most in the 10th year?
Let’s consider Daniel first. In year one, we are told he is paid 28,000 pounds. He has a three percent pay increase each year. One way of approaching this problem would be to find three percent of 28,000 and add it on. This would give the amount he is paid in the second year. We could then repeat this process by finding three percent of this new amount to calculate how much he is paid in the third year. However, as we want the amount that he is paid in the 10th year, this would be very time-consuming. As a result, we will use the following compound interest formula to calculate the amount that Daniel is paid in the 10th year.
𝐴 will be the new value after 10 years, 𝑃 is the principal amount or original value, 𝑟 will be the increase as a decimal, and 𝑡 is the time. The original value is 28,000 as this is the amount Daniel was paid in the first year. Three percent written as a decimal is 0.03 as we divide the percentage by 100. 𝑡 is equal to 10 as we are looking for the amount in the 10th year. We need to calculate 28,000 multiplied by 1.03 to the 10th power. This is equal to 37,629.658 and so on. As we are dealing in money, we need to round this to two decimal places. Daniel will be paid 37,629 pounds and 66 pence in the 10th year.
We are told that Ethan is paid 30,000 in the first year. He gets an increase of 1,250 pounds every two years. This means after 10 years this will have increased five times. Ethan’s salary will have increased by 6,250 pounds. This means that in the 10th year, he will be paid 36,250 pounds.
37,629.66 is greater than 36,250. This means that in the 10th year, Daniel is being paid more than Ethan. The correct answer is Daniel.
