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.

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 Hence, the calculation for should include the withdrawn money in which is, .## Step 5:Now we substitute the given values on the formula:**\( \ P1 = A/(1 + r)^{n}\)**Substituting **\(P1 =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