### 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.