A 10-year bond with a face value of $1,000 has a coupon rate of 6 percent, with interest payments made semi-annually. The bond was issued 3 years ago. The current market interest rate is 9 percent. What is the price that you can expect to get if you choose to sell this bond now ($)

= 846.6576207

Explanation:

The price of a bond is the present value (PV) of the future cash inflows expected from the bond discounted using the yield to maturity.

These cash flows include interest payment and redemption value

The price of the bond can be calculated as follows:

Step 1

PV of interest payment

Semi-annual coupon rate = 6%/2 = 3%

Semi-annual Interest payment =( 3%×$1000)= $30

Semi annual yield = 9%/2 = 4.5%

PV of interest payment

= A ×(1- (1+r)^(-n))/r

Note that the the bond was issued 3 years ago, therefore the time to maturity = 10 -3 = 7 years

A- interest payment, r- yield - 4.5%, n- no of periods- 2 × 7 = 14 periods

= 30× (1-(1.045)^(-7×2))/0.045)

= 30× 10.22282528

=$ 306.6847585

Step 2

PV of redemption value (RV)

PV = RV × (1+r)^(-n)

RV - redemption value- $1000, n- 7, r- 4.5%

= 1,000 × (1+0.045)^(-2×7)

= 539.97

Step 3

Price of bond = PV of interest payment + PV of RV

$ 306.68 + 539.97

= $846.6576207

Price to get if the bond is sold $846.66

Explanation:

Face value of the bond $1000

Cr = 6%

r = 9%

n = 10 but the bond was issued 3 years  ago so it has 7 years remaining to maturity semiannual = 7*2 = 14

Coupons payments are made semi annualy

C = 6%*1000/2 = $30

r = 9%/2 = 4.5%

BV  = C* 1-(1+r)^-n/r + FV/ (1+r)^n

        =30* 1-(1+0.045)^-17/0.045 +1000/(1+0.045)^14

        =306.6848+ 539.9729

         =$846.66

The bond wil trade below par since coupon rate is lower than market rate

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