### Consider the different investment options

To compare the different investment options, we need to calculate the following for each option at the end of the seven year period:

- The future value of the monthly payments.
- The total amount paid into the investment fund.
- The total interest earned.

\[F = \frac{x\left[(1 + i)^{n}-1\right]}{i}\]

**TBS Investments:**

\begin{align*}
F &= \frac{\text{450}\left[(1 + \frac{\text{0,135}}{12})^{84}-1\right]}{\frac{\text{0,135}}{12}} \\
&= \text{R}\,\text{62 370,99} \\
\text{Total amount } (T): \enspace &= 7 \times 12 \times \text{R}\,\text{450} \\
&= \text{R}\,\text{37 800} \\
\text{Total interest } (I): \enspace &= \text{R}\,\text{62 370,99} - \text{R}\,\text{37 800} \\
&= \text{R}\,\text{24 570,99}
\end{align*}

**Taylor Anderson:**

\begin{align*}
F &= \frac{\text{555}\left[(1 + \frac{\text{0,13}}{12})^{84}-1\right]}{\frac{\text{0,13}}{12}} \\
&= \text{R}\,\text{75 421,65} \\
\text{Total amount } (T): \enspace &= 7 \times 12 \times \text{R}\,\text{555} \\
&= \text{R}\,\text{46 620} \\
\text{Total interest } (I): \enspace &= \text{R}\,\text{75 421,65} - \text{R}\,\text{46 620} \\
&= \text{R}\,\text{28 801,65}
\end{align*}

**PHK:**

\begin{align*}
F &= \frac{\text{575}\left[(1 + \frac{\text{0,125}}{12})^{84}-1\right]}{\frac{\text{0,125}}{12}} \\
&= \text{R}\,\text{76 619,96} \\
\text{Total amount } (T): \enspace &= 7 \times 12 \times \text{R}\,\text{575} \\
&= \text{R}\,\text{48 300} \\
\text{Total interest } (I): \enspace &= \text{R}\,\text{76 619,96} - \text{R}\,\text{48 300} \\
&= \text{R}\,\text{28 319,96}
\end{align*}

**Simfords Consulting:**

\begin{align*}
F &= \frac{\text{600}\left[(1 + \frac{\text{0,11}}{12})^{84}-1\right]}{\frac{\text{0,11}}{12}} \\
&= \text{R}\,\text{75 416,96} \\
\text{Total amount } (T): \enspace &= 7 \times 12 \times \text{R}\,\text{600} \\
&= \text{R}\,\text{50 400} \\
\text{Total interest } (I): \enspace &= \text{R}\,\text{75 416,96} - \text{R}\,\text{50 400} \\
&= \text{R}\,\text{25 016,96}
\end{align*}