Shamila, a teacher at a local high school, is going on retirement - NSC Mathematical Literacy - Question 5 - 2022 - Paper 1

If Shamila chooses Option 1, she can withdraw a third of her pension fund benefit. This is calculated as follows:

rac{1}{3} imes R 3 457 920 = R 1 152 640

Thus, Shamila can withdraw R 1 152 640.

To verify Shamila's statement regarding her tax:

1. Calculate the tax payable on R 3 457 920.
2. The taxable income is R 3 457 920, which falls into the highest tax bracket (1 050 001 and above).
3. Thus, the tax is calculated as:

$$130 500 + 0.36 imes (R 3 457 920 - R 1 050 000) = 130 500 + 0.36 imes R 2 407 920$$

4. Simplifying this:

$$= 130 500 + R 867 861.20 = R 998 361.20$$

5. Since R 998 361.20 is less than R 1 000 000, her statement is NOT CORRECT.

To find the loan amount that Suraya will borrow, we use the ratio of the estimated value of Shamila's pension to her daughter's loan amount:

Let the loan amount be L.

Thus,

rac{3 457 920}{L} = 9.9789 ext{ (approx.)}

Rearranging gives:

$$L imes 9.9789 = 3 457 920$$

dividing by 9.9789:

L = rac{3 457 920}{9.9789} ext{ which approximates to } R 346 000.

Thus, rounding to the nearest thousand rand, Suraya will borrow R 346 000.