1. **State the problem:** We want to complete the proof for the formula $$n = \log_{1+i} \left( \frac{iFV}{R} + 1 \right)$$ starting from the given equation: $$R \times \frac{(1+i)^n - 1}{i} = FV$$ 2. **Given equation:** $$R \times \frac{(1+i)^n - 1}{i} = FV$$ 3. **Multiply both sides by $\frac{i}{R}$:** Multiply both sides by $\frac{i}{R}$ to isolate the term with the exponent: $$\frac{i}{R} \times R \times \frac{(1+i)^n - 1}{i} = \frac{i}{R} \times FV$$ Simplify the left side: $$\frac{i}{R} \times R \times \frac{(1+i)^n - 1}{i} = (1+i)^n - 1$$ So, $$ (1+i)^n - 1 = \frac{iFV}{R} $$ 4. **Add 1 to both sides:** $$ (1+i)^n = \frac{iFV}{R} + 1 $$ 5. **Apply the definition of logarithm:** Taking logarithm base $1+i$ on both sides to solve for $n$: $$ n = \log_{1+i} \left( \frac{iFV}{R} + 1 \right) $$ **Final answer:** $$ n = \log_{1+i} \left( \frac{iFV}{R} + 1 \right) $$ This completes the proof. Each step follows algebraic manipulation rules and the definition of logarithm to isolate $n$.