(c) \( \$ 150 \) simple interest is paid on a loan of \( \$ 1500 \) at the rate of \( 5 \% \) p.a. Find the length of the loan \( (T) \)

To find the length of the loan \( T \), we can use the formula for simple interest: \[ I = P \times r \times T \] Where: - \( I \) is the interest earned (or paid), - \( P \) is the principal amount (the initial loan), - \( r \) is the rate of interest per year (in decimal), and - \( T \) is the time in years. From the information provided: - \( I = \$150 \) - \( P = \$1500 \) - \( r = 5\% = 0.05 \) Rearranging the formula to solve for \( T \) gives us: \[ T = \frac{I}{P \times r} \] Substituting the values: \[ T = \frac{150}{1500 \times 0.05} = \frac{150}{75} = 2 \text{ years} \] So, the length of the loan \( T \) is \( 2 \) years.