Find the present value of a 30-year bond that pays an annual coupon,has a coupon rate of 6 percent,a yield to maturity of 5 percent,a par value of €1,000 when the yield to maturity is 5 percent.

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The present value of a bond can be calculated using the formula for the present value of an annuity (for the coupon payments) plus the present value of a lump sum (for the par value at maturity). The coupon payment is 6% of €1,000, which is €60 annually. The yield to maturity is 5%. The formula for the present value of an annuity is $PV = PMT \times \left(1 - (1 + r)^{-n}\right) / r$, where PMT is the annual payment (€60), r is the yield to maturity (5% or 0.05), and n is the number of periods (30 years). The present value of the par value is calculated using the formula $PV = F / (1 + r)^n$, where F is the face value (€1,000).The present value of the coupon payments is:$$PV_{coupons} = €60 \times \left(1 - (1 + 0.05)^{-30}\right) / 0.05 = €60 \times 15.37245 = €922.35$$The present value of the par value is:$$PV_{par} = €1,000 / (1 + 0.05)^{30} = €1,000 / 4.32194 = €231.38$$Adding these two components gives the total present value of the bond:$$PV_{total} = €922.35 + €231.38 = €1,153.73$$

Find the Present Value of a 30-Year Bond That Pays