Question

2) Ayanda wants to invest R200 000. The bank offers him 2 options for his

6 year investment.
Option 1: 12% Simple interest p.a.
Option 2: 9,5% Compound interest p.a.
4.2.1) Calculate the return on Ayanda's investment using Option 1.
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4.2.2) Calculate the return on Ayanda's investment using Option 2.
4.2.3) Which option will render the most money?

Answer 1

4.2.1) R140 000

4.2.2) R144 758.28

4.2.3) Option 2

Explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

`\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}}`

Given values:

• P = R200 000
• r = 12% = 0.12
• t = 6 years

Substitute the given values into the formula and solve for I:

`I=200000 \cdot 0.12 \cdot 6`

`I=24000 \cdot 6`

`I=144000`

Therefore, the return on Ayanda's investment using Option 1 is R144000.

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To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

`\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}}`

Given values:

• P = R200 000
• r = 9.5% = 0.095
• t = 6 years

Substitute the given values into the formula and solve for I:

`I=200000(1+0.095)^6-200000`

`I=200000(1.095)^6-200000`

`I=200000(1.72379142...)-200000`

`I=344758.28426...-200000`

`I=144758.28426...`

`I=144758.28`

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

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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.