QUESTION 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 then changed to \( 10 \% \) p.a. compounded quarterly. Determine the value of the investment after the 7 -year period. 2.2 Convert an interest rate of \( 10 \% \) p.a. compounded quarterly to an annual effective interest rate. 2.3 A lawnmower was traded in for R236 after 10 years. The depreciation was calculated at \( 9,2 \% \) p.a. on a straight-line basis. Determine the cost of the lawnmower 10 years ago.

Investing magic happens when you grasp the power of compound interest! When Boitumelo invested R28,000 for 7 years, the first 2 years of a 12% interest rate compounded semi-annually means interest is added twice a year at 6%, setting a solid foundation for growth. Switching to 10% compounded quarterly for the remaining 5 years means it will be compounded every 3 months at a rate of 2.5% each time. Running those calculations will reveal just how far that initial investment can soar! To convert the \(10\%\) p.a. compounded quarterly into an effective annual rate (EAR), you need to use the formula \((1 + \frac{r}{n})^n - 1\), where \(r\) is the nominal rate as a decimal (0.10 in this case) and \(n\) is the number of compounding periods per year (4). So, plugging in the numbers gives you \((1 + \frac{0.10}{4})^4 - 1\). Solve for that, and you'll find the equivalent interest rate that reflects the true return after a year—definitely a nifty way to visualize your gains!