1. **State the problem:** Calculate the actual interest earned after 35 days on a principal of 100000 with an annual interest rate of 2.5%, considering a 20% tax on the interest. 2. **Formula for simple interest:** $$I = P \times r \times t$$ where $I$ is interest, $P$ is principal, $r$ is annual interest rate (in decimal), and $t$ is time in years. 3. **Convert given values:** - Principal $P = 100000$ - Annual interest rate $r = 2.5\% = 0.025$ - Time $t = \frac{35}{365}$ years (since 35 days) 4. **Calculate gross interest:** $$I = 100000 \times 0.025 \times \frac{35}{365} = 100000 \times 0.025 \times 0.09589 = 239.73$$ 5. **Calculate tax on interest:** Tax rate = 20% = 0.20 $$\text{Tax} = 239.73 \times 0.20 = 47.95$$ 6. **Calculate net interest (actual interest earned):** $$\text{Net Interest} = 239.73 - 47.95 = 191.78$$ **Final answer:** The actual interest earned after 35 days, net of 20% tax, is approximately $191.78$.