1. **State the problem:** Cheryl wants to withdraw 34033 after 6 months from a bank account. The interest rate is 2.37% per annum and the tax on interest is 30%. We need to find how much she must deposit today. 2. **Identify variables:** - Final amount $A = 34033$ - Time $t = 6$ months $= \frac{6}{12} = 0.5$ years - Annual interest rate $r = 2.37\% = 0.0237$ - Tax rate on interest $\text{tax} = 30\% = 0.30$ 3. **Calculate effective growth due to interest and tax:** The interest earned in 6 months before tax is $\text{Interest} = P \times r \times t$ Tax reduces this interest by 30%, so after tax, interest earned is $\text{Interest after tax} = \text{Interest} \times (1 - 0.30) = P \times r \times t \times 0.70$ 4. **Write the total amount after 6 months:** $$ A = P + P \times r \times t \times 0.70 = P (1 + r t (1 - \text{tax})) $$ 5. **Rearrange to find principal $P$:** $$ P = \frac{A}{1 + r t (1 - \text{tax})} = \frac{34033}{1 + 0.0237 \times 0.5 \times 0.7} $$ 6. **Calculate denominator:** $$1 + 0.0237 \times 0.5 \times 0.7 = 1 + 0.008295 = 1.008295$$ 7. **Calculate principal:** $$ P = \frac{34033}{1.008295} \approx 33708.10 $$ **Final answer:** Cheryl must deposit **33708.10** today to withdraw 34033 after 6 months considering the tax on interest.