EXERCISE 3 (a) Arnold paid R2 599,99 for a car sound system in 1997. Assuming an average inflation rate of \( 7 \% \) per annum, what did he pay for a sound system with the equivalent value in \( 2014 ? \)

To calculate the equivalent value of the car sound system in 2014, we can use the formula for future value based on inflation: \[ FV = PV \times (1 + r)^n \] Where: - \( FV \) = future value - \( PV \) = present value (initial amount) - \( r \) = inflation rate (as a decimal) - \( n \) = number of years In this case: - \( PV = R2,599.99 \) - \( r = 0.07 \) (7% as a decimal) - \( n = 2014 - 1997 = 17 \) years Now, we can plug in the values: \[ FV = 2599.99 \times (1 + 0.07)^{17} \] Calculating \( (1 + 0.07)^{17} \): \[ (1 + 0.07)^{17} \approx 3.368 \] Now, we can calculate the future value: \[ FV \approx 2599.99 \times 3.368 \approx 8,748.66 \] Therefore, the equivalent value of the car sound system in 2014 is approximately **R8,748.66**.