4. \( \$ 670 \) is invested at \( 8 \% \) p.a simple interest. Dave wants to know the number of years it will take the investment to grow to \( \$ 991.64 \). Calculate the interest that will be earned on the investment. 4a. 4b Calculate the number of years \( T \) it will take the investment to grow to \( \$ 991.60 \). Enter each line of working as an equation, and give your answer to the nearest whole number. \( T= \)

To find the interest that will be earned on the investment, we can start with the formula for simple interest: \[ I = P \cdot r \cdot T \] where: - \( I \) is the interest, - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (as a decimal), - \( T \) is the time in years. 1. **Calculate the interest**: - The total amount after interest is \( A = 991.64 \) (final amount). - The formula relating final amount, principal, and interest is: \[ A = P + I \Rightarrow I = A - P = 991.64 - 670 = 321.64 \] - Therefore, the interest earned on the investment is \( I = \$321.64 \). 2. **To calculate the number of years \( T \)**, we rearrange the interest formula: \[ T = \frac{I}{P \cdot r} \] - We already know that \( I = 321.64 \), \( P = 670 \), and \( r = 0.08 \): \[ T = \frac{321.64}{670 \cdot 0.08} = \frac{321.64}{53.6} \approx 6 \] Thus, the answer is \( T \approx 6 \) years when rounded to the nearest whole number.