1. **Stating the problem:** Cheryl wants to withdraw 34033 after 6 months from a bank account. The interest rate is 2.37% per annum and a tax at source of 30% applies to the earned interest. 2. **Identify variables:** - Withdrawal amount (future value) $FV = 34033$ - Interest rate per year $r = 0.0237$ - Tax rate on interest $t = 0.30$ - Time period in years $T = \frac{6}{12} = 0.5$ 3. **Calculate the net interest after tax:** The interest earned before tax over 6 months is $$FV - P$$ where $P$ is the principal (initial deposit). Interest after tax is $$(FV - P)(1 - t)$$. 4. **Set up the compound interest equation:** Since interest is simple over 6 months, the amount after 6 months is: $$FV = P + P \cdot r \cdot T \cdot (1 - t)$$ where $P$ is the principal to find. 5. **Solve for $P$:** $$ FV = P (1 + r \cdot T \cdot (1 - t)) $$ $$ P = \frac{FV}{1 + r \cdot T \cdot (1 - t)} $$ 6. **Substitute values:** $$ P = \frac{34033}{1 + 0.0237 \cdot 0.5 \cdot (1 - 0.30)} = \frac{34033}{1 + 0.0237 \cdot 0.5 \cdot 0.7} $$ Calculate the denominator: $$ 1 + 0.0237 \times 0.5 \times 0.7 = 1 + 0.008295 = 1.008295 $$ 7. **Calculate $P$:** $$ P = \frac{34033}{1.008295} \approx 33710.62 $$ **Final answer:** Cheryl must deposit approximately 33710.62 today to be able to withdraw 34033 after 6 months, considering interest and tax.