1. **State the problem:** Calculate the amount of P55000 compounded quarterly at an annual interest rate of 12.15% for 9 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 amount - $r$ is the annual interest rate (decimal) - $n$ is the number of times interest is compounded per year - $t$ is the time in years 3. **Identify values:** - $P = 55000$ - $r = 0.1215$ - $n = 4$ (quarterly compounding) - $t = 9$ 4. **Calculate the amount:** $$A = 55000 \left(1 + \frac{0.1215}{4}\right)^{4 \times 9} = 55000 \left(1 + 0.030375\right)^{36} = 55000 \times (1.030375)^{36}$$ 5. **Evaluate the power:** Calculate $(1.030375)^{36}$ using a calculator: $$ (1.030375)^{36} \approx 2.41414 $$ 6. **Multiply to find $A$:** $$ A = 55000 \times 2.41414 = 132777.7 $$ 7. **Interpretation:** The amount after 9 years is approximately P132777.7. Since the question asks for the interest earned or the amount minus principal: 8. **Calculate interest earned:** $$ \text{Interest} = A - P = 132777.7 - 55000 = 77777.7 $$ The options given (P18729.73, P18792.73, P18279.73, P18297.73) do not match the total amount or interest calculated, so it seems the question might be asking for something else or there is a typo. If the question is about the interest earned quarterly compounded, the correct amount is approximately P132777.7. **Final answer:** The amount after 9 years is approximately **P132777.7**.