Question 7.9: Suppose an investor purchases a 5-year €10,000 bond when it ......
Suppose an investor purchases a 5-year €10,000 bond when it is issued on January 1, 2020 at a coupon rate of 6% with interest paid bi-annually, and the market rate of interest is 4%. Determine the value of the bond on July 1, 2023.
The value of the bond is determined from the present value of the remaining interest payments and the present value of the bond maturity amount with respect to the market rate of interest.
There are three remaining interest payments (December 31, 2023; June 30, 2024; and December 31, 2024) and so n = 3, the market rate of interest i = 0.02 as before, and the interest amount is €300 as before.
The present value of the interest payments is given by
300/0.02(1–1/(1.02)³ ) = 15000(0.05767) = €865.16
The present value of the maturity amount is given by the present value formula where n = 3 = 10, and the interest rate i per interest period is 0.02.
PV\ =\ M V\left(1\,+\,i\right)^{-n}= 10000(1.02)^{-3}
= €9423.32
Therefore, the value of the bond on July 1, 2023 is given by the sum of the present value of the remaining interest payments and the present value of the maturity amount:
= €865.16 + €9423.32
= €10,288.37