Verify, with calculations, whether Lerato's claim is valid.

Tax bracket A covers taxable income from R0 to R250 000, with a tax rate of 18% of taxable income. The R45 000 in tax bracket B represents the tax payable on the maximum income of the preceding bracket (Bracket A).

$$\text{Tax on R250 000} = 18\% \times \text{R}250 000$$ $$\text{Tax on R250 000} = 0.18 \times \text{R}250 000$$ $$\text{Tax on R250 000} = \boxed{\text{R}45 000}$$

Sipho's monthly basic salary is R25 220.50. To find the annual gross salary, multiply the monthly salary by 12.

$$\text{Annual Gross Salary} = \text{R}25 220.50 \times 12$$ $$\text{Annual Gross Salary} = \boxed{\text{R}302 646.00}$$

Sipho's annual gross salary is R302 646.00.
Referring to TABLE 3:

• Bracket A: R0 – R250 000
• Bracket B: R250 001 – R400 000
• Bracket C: R400 001 – R550 000 Since R302 646.00 falls between R250 001 and R400 000, Sipho falls into $\boxed{\text{Tax Bracket B}}$.

Sipho is 69 years old, so he qualifies for both the Primary Rebate and the Secondary Rebate.

$$\text{Primary Rebate} = \text{R}17 235$$ $$\text{Secondary Rebate} = \text{R}9 444$$ $$\text{Total Tax Rebates} = \text{R}17 235 + \text{R}9 444$$ $$\text{Total Tax Rebates} = \boxed{\text{R}26 679}$$

First, calculate the annual tax payable before rebates and medical tax credits.
Sipho's annual gross salary is R302 646.00, which is in Tax Bracket B.

$$\text{Tax Payable (before rebates)} = \text{R}45 000 + 26\% \text{ of the amount above R250 000}$$ $$\text{Amount above R250 000} = \text{R}302 646 - \text{R}250 000 = \text{R}52 646$$ $$\text{Tax Payable (before rebates)} = \text{R}45 000 + (0.26 \times \text{R}52 646)$$ $$\text{Tax Payable (before rebates)} = \text{R}45 000 + \text{R}13 687.96$$ $$\text{Tax Payable (before rebates)} = \text{R}58 687.96$$

Next, subtract the total tax rebates.

$$\text{Tax Payable (after rebates)} = \text{R}58 687.96 - \text{R}26 679$$ $$\text{Tax Payable (after rebates)} = \text{R}32 008.96$$

Next, calculate the annual medical tax credits. Sipho covers himself (main member) and his two children (first dependent and additional member).

$$\text{Monthly Medical Tax Credit} = \text{R}364 (\text{main member}) + \text{R}364 (\text{first dependent}) + \text{R}246 (\text{additional member})$$ $$\text{Monthly Medical Tax Credit} = \text{R}974$$ $$\text{Annual Medical Tax Credit} = \text{R}974 \times 12$$ $$\text{Annual Medical Tax Credit} = \text{R}11 688$$

Now, calculate the final annual tax payable.

$$\text{Final Annual Tax Payable} = \text{Tax Payable (after rebates)} - \text{Annual Medical Tax Credit}$$ $$\text{Final Annual Tax Payable} = \text{R}32 008.96 - \text{R}11 688$$ $$\text{Final Annual Tax Payable} = \text{R}20 320.96$$

Finally, calculate the final monthly tax payable.

$$\text{Final Monthly Tax Payable} = \frac{\text{R}20 320.96}{12}$$ $$\text{Final Monthly Tax Payable} = \text{R}1 693.41$$

Sipho claims his final monthly tax payable is above R1 800. Since R1 693.41 is not above R1 800, Sipho's claim is $\boxed{\text{invalid}}$.

Lerato invests R72 000 for 2 years (as per the claim).

• Option 1: Mandla Bank (Simple Interest) Principal ($P$) = R72 000 Interest rate ($i$) = 7.5% p.a. = 0.075 Time ($n$) = 2 years The formula for simple interest amount is $A = P(1 + i \cdot n)$.

  $$A_1 = \text{R}72 000 (1 + 0.075 \times 2)$$ $$A_1 = \text{R}72 000 (1 + 0.15)$$ $$A_1 = \text{R}72 000 (1.15)$$ $$A_1 = \text{R}82 800$$ $$\text{Interest earned} = A_1 - P = \text{R}82 800 - \text{R}72 000 = \text{R}10 800$$

• Option 2: Thato Bank (Compound Interest) Principal ($P$) = R72 000 Interest rate ($i$) = 8.8% p.a. compounded annually = 0.088 Time ($n$) = 2 years The formula for compound interest amount is $A = P(1 + i)^n$.

  $$A_2 = \text{R}72 000 (1 + 0.088)^2$$ $$A_2 = \text{R}72 000 (1.088)^2$$ $$A_2 = \text{R}72 000 (1.183744)$$ $$A_2 = \text{R}85 229.568$$

  Rounding to two decimal places: $A_2 = \text{R}85 229.57$

  $$\text{Interest earned} = A_2 - P = \text{R}85 229.57 - \text{R}72 000 = \text{R}13 229.57$$

Comparing the interest earned after 2 years:
Mandla Bank: R10 800
Thato Bank: R13 229.57
Since R13 229.57 > R10 800, Thato Bank earns more interest.
Therefore, Lerato's claim that Thato Bank will be the better option because she will earn more interest after 2 years is $\boxed{\text{valid}}$.