On the 1st January 2014 Jill invested some money in a bank account. The account pays 3.5% compound I interest per year. On 1st January 2015 Jill withdrew ￡3000 from the account. On 1st January 2016 she had ￡66310.38 in the account. Work out how much Jill originally invested in the account.

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On the 1st January 2014 Jill invested some money in a bank account. The account pays 3.5% compound I interest per year. On 1st January 2015 Jill withdrew ￡3000 from the account. On 1st January 2016 she had ￡66310.38 in the account. Work out how much Jill originally invested in the account.

Answer 1

Using the above equation, we find than Jill initially deposited: ** [ insert your result after calculation ]** in her account.

Answer 2

## Step 1: We know that for compound interest, the formula to be used is: ### **\(A = P(1 + r)^{n} \)** Here \( A \) is the final amount in the account, \( P \) is the principal amount (initial amount) Jill had initially invested in the bank, \( r \) is the annual interest rate expressed as a decimal, and \( n \) is the total years the money was invested. ## Step 2: As we know \( A \) and \( r \), we rewrite the formula to find \( P, the principal amount as: ### **\( P = \frac { A }{(1 + r)^{n}}\)** This provides the approach to calculate \(P\). ## Step 3: We first calculate the principal amount (\(P1 \)) In the year \( 2015\). Here \(r \) is \( 0.035\), \(n \) is \( 2\), and \(A \) is the total amount calculated after \( 2\) years \((2016)\) which is \(£ 66310.38\). ## Step 4: While calculating \(A \), we should remember that in the year \( 2015\) Jill also withdrew \(£ 3000 \). Hence, the calculation for \( A \) should include the withdrawn money in \( 2015\) which is, \(A = 66310.38 + 3000 = £69310.38 \). ## Step 5: Now we substitute the given values on the formula: **\( \ P1 = A/(1 + r)^{n}\)** Substituting **\(P1 = £69310.38/(1+0.035)^{2}\) The result should be the initial amount Jill Invested.

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On the 1st January 2014 Jill invested some money in a bank account. The account pays 3.5% compound I interest per year. On 1st January 2015 Jill withdrew ￡3000 from the account. On 1st January 2016 she had ￡66310.38 in the account. Work out how much Jill originally invested in the account.

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