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 nominal annual interest rate is 7%, 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), and deposits are every 4 months, the deposits and compounding periods do not align perfectly. We treat this as an annuity with deposits every 4 months and interest compounded quarterly. 4. **Convert interest rate to effective rate per deposit period:** The effective interest rate per 4 months (one deposit period) is calculated by compounding quarterly rates for 4 months (which is $\frac{4}{3}$ quarters): $$ i = \left(1 + 0.0175\right)^{\frac{4}{3}} - 1 $$ Calculate this: $$ i = (1.0175)^{1.3333} - 1 $$ 5. **Use the future value of an annuity formula:** $$ FV = P \times \frac{(1+i)^n - 1}{i} $$ where $P=230$, $n=27$, and $i$ is the effective interest rate per deposit period. 6. **Substitute values:** $$ FV = 230 \times \frac{\left( (1.0175)^{\frac{4}{3}} \right)^{27} - 1}{(1.0175)^{\frac{4}{3}} - 1} $$ 7. **Simplify the exponent:** $$ \left( (1.0175)^{\frac{4}{3}} \right)^{27} = (1.0175)^{36} $$ because $\frac{4}{3} \times 27 = 36$ quarters. 8. **Final exact formula:** $$ FV = 230 \times \frac{(1.0175)^{36} - 1}{(1.0175)^{\frac{4}{3}} - 1} $$ This is the exact amount in the account at the end of 9 years. **Answer:** $$ \boxed{230 \times \frac{(1.0175)^{36} - 1}{(1.0175)^{\frac{4}{3}} - 1}} $$