1. **State the problem:** Calculate the future value of end-of-quarter payments of 9000 made at an interest rate of 2.14% compounded monthly for 5 years. 2. **Identify the formula:** Since payments are made at the end of each quarter and interest is compounded monthly, we use the future value of an annuity formula adjusted for compounding periods: $$FV = P \times \frac{(1 + r/n)^{nt} - 1}{(1 + r/n)^{m} - 1}$$ where: - $P = 9000$ (payment per quarter) - $r = 0.0214$ (annual interest rate as a decimal) - $n = 12$ (compounding periods per year, monthly) - $t = 5$ (years) - $m = 3$ (number of months per quarter, since payments are quarterly) 3. **Calculate the components:** - Monthly interest rate: $r/n = 0.0214 / 12 = 0.0017833333$ - Total compounding periods: $nt = 12 \times 5 = 60$ - Number of months per payment period: $m = 3$ 4. **Calculate the numerator:** $$ (1 + 0.0017833333)^{60} - 1 = (1.0017833333)^{60} - 1 $$ Calculate $ (1.0017833333)^{60} \approx 1.1136$, so numerator $= 1.1136 - 1 = 0.1136$ 5. **Calculate the denominator:** $$ (1 + 0.0017833333)^3 - 1 = (1.0017833333)^3 - 1 $$ Calculate $ (1.0017833333)^3 \approx 1.00536$, so denominator $= 1.00536 - 1 = 0.00536$ 6. **Calculate the fraction:** $$ \frac{0.1136}{0.00536} \approx 21.1940$$ 7. **Calculate the future value:** $$ FV = 9000 \times 21.1940 = 190746$$ 8. **Round to nearest cent:** $$ FV \approx 190746.00 $$ **Final answer:** The future value of the quarterly payments is approximately 190746.00.