\( \mathrm{A}=\mathrm{P}(1+i)^{n} \) \( \therefore 400000=\mathrm{P}(1+0,15)^{5} \quad \) Substitute known value

\[ \textbf{Step 1: Write the formula.} \] The compound interest formula is given by \[ A = P(1+i)^n. \] \[ \textbf{Step 2: Substitute known values.} \] We have \( A = 400000 \), \( i = 0.15 \), and \( n = 5 \). Substituting these values in, we get \[ 400000 = P(1+0.15)^5 \quad \Longrightarrow \quad 400000 = P(1.15)^5. \] \[ \textbf{Step 3: Solve for } P. \] Dividing both sides by \( (1.15)^5 \) gives \[ P = \frac{400000}{(1.15)^5}. \] \[ \textbf{Step 4: Calculating } (1.15)^5. \] We calculate \[ (1.15)^5 \approx 2.01136. \] \[ \textbf{Step 5: Substitute the approximate value back.} \] Thus, \[ P \approx \frac{400000}{2.01136} \approx 198706.4. \] \[ \textbf{Final Answer:} \quad P \approx 198706.4. \]