Video: Pack 4 • Paper 3 • Question 4

Pack 4 • Paper 3 • Question 4

03:06

Video Transcript

Harry and Gemma both have 15000 pounds to invest. Harry invests his money in the Golden Lion bank and Gemma invests her money in the Silver Serpent bank. At the end of three years, who will have made the greatest profit? The Golden Lion bank has compound interest of three percent for each year, whereas the Silver Serpent bank has compound interest of 6.6 percent for the first year, but 1.4 percent for each extra year.

If we firstly consider Harry and the Golden Lion bank, three percent compound interest means that the multiplier is 1.03. This is because three percent plus 100 percent is 103 percent and 103 percent as a decimal is 1.03. As Harry is investing his money for three years, the total amount after this period of time will be given by 15000 multiplied by 1.03 multiplied by 1.03 multiplied by 1.03 again. This can be rewritten as 15000 multiplied by 1.03 cubed. This gives us 16390.91 to two decimal places. This means that after three years, Harry will have 16390 pounds and 91 pence.

The Silver Serpent bank has two different interest rates: 6.6 percent for the first year and 1.4 percent for each extra year. This means that our multiplier will be 1.066 for 6.6 percent and 1.014 for 1.4 percent. This means that the total amount of money that Gemma will have after three years is given by 15000 multiplied by 1.066 multiplied by 1.014 squared as she will get 6.6 percent interest for the first year and 1.4 percent interest for the following two years. This is equal to 16440.85 to two decimal places. Therefore, after three years, Gemma will have 16440 pounds and 85 pence.

As 16390.91 is less than 16440.85, after three years, Harry will have less than Gemma. This means that Gemma has made the greatest profit.

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