1. **State the problem:** A manager invests 5000 each year for 4 years buying securities at different prices. We need to find the average price paid per security over the 4 years. 2. **Formula:** The average price paid is the total amount invested divided by the total number of securities bought. 3. **Calculate the number of securities bought each year:** - Year 1: $ \frac{5000}{62} $ - Year 2: $ \frac{5000}{76} $ - Year 3: $ \frac{5000}{84} $ - Year 4: $ \frac{5000}{90} $ 4. **Calculate total securities bought:** $$ \frac{5000}{62} + \frac{5000}{76} + \frac{5000}{84} + \frac{5000}{90} $$ 5. **Calculate total amount invested:** $$ 5000 \times 4 = 20000 $$ 6. **Calculate average price:** $$ \text{Average price} = \frac{\text{Total amount invested}}{\text{Total securities bought}} = \frac{20000}{\frac{5000}{62} + \frac{5000}{76} + \frac{5000}{84} + \frac{5000}{90}} $$ 7. **Simplify denominator by factoring out 5000:** $$ \frac{20000}{5000 \left( \frac{1}{62} + \frac{1}{76} + \frac{1}{84} + \frac{1}{90} \right)} = \frac{20000}{5000} \times \frac{1}{\frac{1}{62} + \frac{1}{76} + \frac{1}{84} + \frac{1}{90}} $$ 8. **Simplify:** $$ \cancel{\frac{20000}{5000}} \times \frac{1}{\frac{1}{62} + \frac{1}{76} + \frac{1}{84} + \frac{1}{90}} = 4 \times \frac{1}{\frac{1}{62} + \frac{1}{76} + \frac{1}{84} + \frac{1}{90}} $$ 9. **Calculate sum of reciprocals:** $$ \frac{1}{62} + \frac{1}{76} + \frac{1}{84} + \frac{1}{90} \approx 0.01613 + 0.01316 + 0.01190 + 0.01111 = 0.0523 $$ 10. **Calculate average price:** $$ 4 \times \frac{1}{0.0523} = 4 \times 19.12 = 76.48 $$ **Final answer:** The average price paid for the security is approximately **76.48**.