1. **Problem statement:** An investor makes quarterly payments of 192 into an annuity that earns 5.3% annual interest compounded quarterly. Payments are made at the end of each quarter for 15 years. We need to find the total value of the annuity at the end of 15 years. 2. **Formula used:** The future value of an ordinary annuity (payments at the end of each period) is given by: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $P$ = payment per period - $r$ = interest rate per period - $n$ = total number of payments 3. **Identify values:** - Annual interest rate = 5.3% = 0.053 - Compounded quarterly means 4 periods per year - Interest rate per quarter $r = \frac{0.053}{4} = 0.01325$ - Number of quarters in 15 years $n = 15 \times 4 = 60$ - Payment per quarter $P = 192$ 4. **Calculate future value:** $$FV = 192 \times \frac{(1 + 0.01325)^{60} - 1}{0.01325}$$ 5. **Calculate $(1 + 0.01325)^{60}$:** $$1.01325^{60} \approx 2.197364$$ 6. **Substitute back:** $$FV = 192 \times \frac{2.197364 - 1}{0.01325} = 192 \times \frac{1.197364}{0.01325}$$ 7. **Divide:** $$\frac{1.197364}{0.01325} \approx 90.3784$$ 8. **Multiply:** $$192 \times 90.3784 \approx 17351.65$$ **Final answer:** The total value of the annuity after 15 years is approximately **17351.65**.