1. **Problem statement:** Find the present value of an annuity due that pays 4000 at the beginning of each quarter for 7 years with an interest rate of 5.4% compounded quarterly. 2. **Formula:** The present value of an annuity due is given by $$PV = P \times \frac{1 - (1 + r)^{-n}}{r} \times (1 + r)$$ where: - $P$ is the payment per period, - $r$ is the interest rate per period, - $n$ is the total number of payments. 3. **Calculate parameters:** - Annual interest rate = 5.4% = 0.054 - Quarterly interest rate $r = \frac{0.054}{4} = 0.0135$ - Number of quarters $n = 7 \times 4 = 28$ - Payment per quarter $P = 4000$ 4. **Substitute values:** $$PV = 4000 \times \frac{1 - (1 + 0.0135)^{-28}}{0.0135} \times (1 + 0.0135)$$ 5. **Calculate $(1 + 0.0135)^{-28}$:** $$ (1.0135)^{-28} = \frac{1}{(1.0135)^{28}} \approx \frac{1}{1.432364} = 0.6985$$ 6. **Calculate numerator:** $$1 - 0.6985 = 0.3015$$ 7. **Calculate fraction:** $$\frac{0.3015}{0.0135} \approx 22.3333$$ 8. **Multiply by $(1 + r)$:** $$22.3333 \times 1.0135 = 22.6333$$ 9. **Multiply by payment $P$:** $$4000 \times 22.6333 = 90533.20$$ **Final answer:** The present value of the annuity due is approximately **90533.20**.