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# If £2000 is placed into a bank account that pays 3% compound intrest per year, how much will be in the account after 2 years?

There are 2 ways we could solve this question. THE LONG WAY: We add 3% to the capital sum (i.e. 2000 pounds) to find how much money we have after 1 year and then add 3% percent to that sum to find how much you have after two years. If the compound interest is 3% then that essentially means that after 1 year you have 103% of the original i.e. we have 100% of the original which is just the value of the original, plus 3% of the original so 103% in total. If we convert 103% into a decimal by dividing it by 100 we get 1.03. So, to find how much 103% of the capital sum (2000 pounds) is, we have to multiply it by 1.03: 2000 x 1.03 = 2060 So we have 2060 pounds after 1 year. In the second year, further 3 percent are added to the amount we have after 1 year. It is *compound* interest so this means after 2 years we have 103% of 2060 pounds and not 106% of 2000 pounds. To find 103% of 2060 pounds we do: 2060 x 1.03 = 2121.80 pounds This is how much we have in our account after two years. But, we can also do this THE SHORT WAY: Using the formula C*((1+r)^t) where r = interest rate t = the number of years To simplify: 1+r is exactly what we established above: 1.03. It shows what percentage of the original we have after one year expressed in decimal form. So in this case 103% or 1.03. We then raise this value to the number of years so 1.03 to the power of 2 1.03^2 = 1.0609 This number is then multiplied by the capital sum, 2000 pounds: 2000 x 1.0609 = 2121.80 pounds This is the same answer as using the long way. Hope this helps!  Lilli Ganzer
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6(1/2)^n-1

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