1. **State the problem:** Calculate the interest earned on an investment of 250000 compounded semi-annually at an interest rate of 7.05% for 6 years. 2. **Formula used:** The compound interest formula is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after interest - $P$ is the principal (initial investment) - $r$ is the annual interest rate (decimal) - $n$ is the number of compounding periods per year - $t$ is the time in years 3. **Identify values:** - $P = 250000$ - $r = 7.05\% = 0.0705$ - $n = 2$ (semi-annually) - $t = 6$ 4. **Calculate the amount $A$:** $$A = 250000 \left(1 + \frac{0.0705}{2}\right)^{2 \times 6} = 250000 \left(1 + 0.03525\right)^{12} = 250000 \times (1.03525)^{12}$$ 5. **Calculate $(1.03525)^{12}$:** $$ (1.03525)^{12} \approx 1.514546 $$ 6. **Calculate $A$:** $$ A = 250000 \times 1.514546 = 378636.5 $$ 7. **Calculate interest earned:** $$ \text{Interest} = A - P = 378636.5 - 250000 = 128636.5 $$ 8. **Compare with options:** The closest option to 128636.5 is **128638.60**. **Final answer:** The interest earned is **128638.60**.