1. **State the problem:** Calculate the value of a Tk. 5,000 par value bond paying quarterly interest at an annual coupon rate of 10%, with 10 years maturity, when the required rate is 12% annual, compounded quarterly. 2. **Identify given data:** - Par value, $F = 5000$ - Annual coupon rate, $r_c = 10\%$ - Coupon payment frequency: quarterly (4 times a year) - Maturity, $T = 10$ years - Required annual rate, $r_y = 12\%$, compounded quarterly 3. **Calculate coupon payment per quarter:** $$\text{Coupon per quarter} = \frac{r_c \times F}{4} = \frac{0.10 \times 5000}{4} = 125$$ 4. **Calculate number of periods:** $$n = 10 \times 4 = 40$$ 5. **Calculate required rate per period:** $$i = \frac{r_y}{4} = \frac{0.12}{4} = 0.03$$ 6. **Calculate present value of coupon payments (annuity):** $$PV_{coupons} = 125 \times \frac{1 - (1 + 0.03)^{-40}}{0.03}$$ Calculate: $$1 + 0.03 = 1.03$$ $$1.03^{-40} = \frac{1}{1.03^{40}} \approx 0.30656$$ $$1 - 0.30656 = 0.69344$$ $$\frac{0.69344}{0.03} = 23.1147$$ $$PV_{coupons} = 125 \times 23.1147 = 2889.34$$ 7. **Calculate present value of par value (lump sum):** $$PV_{par} = 5000 \times (1.03)^{-40} = 5000 \times 0.30656 = 1532.80$$ 8. **Calculate total bond value:** $$PV = PV_{coupons} + PV_{par} = 2889.34 + 1532.80 = 4422.14$$ **Final answer:** The value of the bond is approximately **Tk. 4422.14**.