1. **State the problem:** A customer deposits 230 every 4 months into an account with 7% annual interest compounded quarterly. We want to find the amount in the account after 9 years. 2. **Identify the interest rate and compounding periods:** The interest rate is 7% per annum compounded quarterly, so the quarterly interest rate is $\frac{7\%}{4} = 1.75\% = 0.0175$. 3. **Determine the number of deposits and compounding periods:** Deposits are made every 4 months, which is every 1/3 of a year. In 9 years, the number of deposits is $\frac{9}{\frac{1}{3}} = 27$ deposits. Since interest is compounded quarterly (every 3 months), the number of quarters in 9 years is $9 \times 4 = 36$ quarters. 4. **Adjust the problem to match compounding and deposit frequency:** Deposits are every 4 months, but compounding is every 3 months. We treat this as an annuity with deposits every 4 months and interest compounded quarterly. 5. **Calculate the future value of the annuity:** The formula for the future value of an annuity with payments $P$ made every $m$ months, interest rate per quarter $i$, and total quarters $n$ is: $$FV = P \times \frac{(1+i)^n - 1}{(1+i)^k - 1}$$ where $k$ is the number of quarters per deposit period. Since deposits are every 4 months and quarters are every 3 months, $k = \frac{4}{3}$ quarters per deposit. 6. **Calculate $k$ and apply the formula:** $$k = \frac{4}{3} \approx 1.3333$$ Number of deposits $= 27$, so total quarters $n = 27 \times k = 27 \times 1.3333 = 36$ quarters (matches the total quarters in 9 years). 7. **Calculate the future value:** $$FV = 230 \times \frac{(1+0.0175)^{36} - 1}{(1+0.0175)^{1.3333} - 1}$$ Calculate numerator: $$(1.0175)^{36} = e^{36 \times \ln(1.0175)} \approx e^{36 \times 0.01735} = e^{0.6246} \approx 1.867$$ So numerator $= 1.867 - 1 = 0.867$ Calculate denominator: $$(1.0175)^{1.3333} = e^{1.3333 \times 0.01735} = e^{0.02313} \approx 1.0234$$ Denominator $= 1.0234 - 1 = 0.0234$ 8. **Compute the fraction:** $$\frac{0.867}{0.0234} \approx 37.05$$ 9. **Calculate final amount:** $$FV = 230 \times 37.05 = 8521.5$$ **Answer:** The amount in the account at the end of 9 years is approximately 8521.5.