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Simon invests some money in a bank account with an interest rate of three percent.
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The interest is compounded annually and the amount of money in Simon’s account after 𝑡 years is 𝑀 𝑡.
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𝑀 zero is equal to 2000 pounds and 𝑀 𝑡 plus one is equal to 𝐾 multiplied by 𝑀 𝑡.
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Find the value of 𝐾.
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Simon is paid interest by the bank annually — that’s each year.
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And this is money that the bank give him in return for investing his money with them.
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The type of interest in this question is compound interest, which means that in future years Simon receives interests not just on his initial investment, but also on the interest he’s already received.
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We’re told that 𝑀 zero is equal to 2000, which means that Simon’s initial investment in the bank account is 2000 pounds.
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We’re then told that the amount of money in Simon’s account after 𝑡 plus one years can be found by multiplying the amount of money in his account after 𝑡 years by this number 𝐾.
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We need to determine the value of 𝐾.
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We’re also told in the question that the interest rate is three percent.
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This means that assuming Simon doesn’t withdraw any money from his account, then each year he will have 100 percent of his starting balance plus an additional three percent paid to him in interest.
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He will, therefore, have 103 percent of the amount that he had the year before.
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To find 103 percent of a number, we have to multiply by the decimal 1.03.
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This is found by dividing 103 by 100.
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This is the value of 𝐾.
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The amount of money in Simon’s account after 𝑡 plus one years is found by multiplying the amount of money in his account after 𝑡 years by 1.03.