STION 2 Boitumelo invests an amount of R28 000 for a period of 7 years. For the first two years the interest was \( 12 \% \) p.a. compounded semi-annually. The interest was the changed to \( 10 \% \) p.a. compounded quarterly. Determine the value of the investment after the 7-year period.

To determine the value of Boitumelo's investment after 7 years, we can break it down into two parts: the first 2 years with \( 12\% \) p.a. compounded semi-annually, and the remaining 5 years with \( 10\% \) p.a. compounded quarterly. **For the first 2 years:** The semi-annual interest rate is \( 12\%/2 = 6\% = 0.06 \). The number of compounding periods for 2 years is \( 2 \times 2 = 4 \). Using the formula for compound interest: \[ A = P(1 + r/n)^{nt} \] Where: - \( P = 28000 \) - \( r = 0.12 \) - \( n = 2 \) (since it's semi-annual) - \( t = 2 \) Substituting the values, we get: \[ A = 28000 (1 + 0.06)^4 \] \[ A \approx 28000 \times 1.26247696 \] \[ A \approx 35349.36 \] **For the next 5 years:** Now, the investment grows at \( 10\% \) p.a. compounded quarterly. The quarterly interest rate is \( 10\%/4 = 2.5\% = 0.025 \). The number of compounding periods for 5 years is \( 5 \times 4 = 20 \). Using the same compound interest formula: \[ P = 35349.36 \] \[ r = 0.10 \] \[ n = 4 \] \[ t = 5 \] We substitute: \[ A = 35349.36 (1 + 0.025)^{20} \] \[ A \approx 35349.36 \times (1.025)^{20} \] \[ A \approx 35349.36 \times 1.28008453 \] \[ A \approx 45238.47 \] Thus, the value of the investment after 7 years is approximately **R45,238.47**.