Answer:
4.2.1) R140 000
4.2.2) R144 758.28
4.2.3) Option 2
Step-by-step explanation:
To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
Substitute the given values into the formula and solve for I:
[tex]I=200000 \cdot 0.12 \cdot 6[/tex]
[tex]I=24000 \cdot 6[/tex]
[tex]I=144000[/tex]
Therefore, the return on Ayanda's investment using Option 1 is R144000.
[tex]\hrulefill[/tex]
To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
Substitute the given values into the formula and solve for I:
[tex]I=200000(1+0.095)^6-200000[/tex]
[tex]I=200000(1.095)^6-200000[/tex]
[tex]I=200000(1.72379142...)-200000[/tex]
[tex]I=344758.28426...-200000[/tex]
[tex]I=144758.28426...[/tex]
[tex]I=144758.28[/tex]
Therefore, the return on Ayanda's investment using Option 2 is R144758.28.
[tex]\hrulefill[/tex]
Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.
