Question

(a) What is the price of a 5.000% semiannual coupon bond with yield to maturity of 4.800% and a tenor of 28 years.

(b) What is the price of a 5.000% semiannual coupon bond with yield to maturity of 4.800% and a tenor of 2 years.

(c) What is happening to the price of the bond as the tenor approaches zero (maturity)? What is this phenomenon called?

Answer 1

(a) \(F V=1,000\)

\(\mathrm{cpn}=1,000 * 0.05 / 2=25\)

\(n=2 * 2=4\)

\(r=4.8 \% / 2=0.024\)

Price \(=\frac{c p n}{r} *\left[1-\frac{1}{(1+r)^{n}}\right]+\frac{F V}{(1+r)^{n}}\)

Price \(=\frac{25}{0.024} *\left[1-\frac{1}{(1+0.024)^{56}}\right]+\frac{1,000}{(1+0.024)^{56}}\)

Price \(=1,041.6666666667 * 0.7350265086+264.9734913689\)

Price \(=\$ 1,030.6261044939\)

b.

\(\mathrm{FV}=1,000\)

\(\mathrm{cpn}=1,000 * 0.05 / 2=25\)

\(n=28 * 2=56\)

\(r=4.8 \% / 2=0.024\)

Price \(=\frac{25}{0.024} *\left[1-\frac{1}{(1+0.024)^{4}}\right]+\frac{1,000}{(1+0.024)^{4}}\)

Price \(=1,041.6666666667 * 0.09050529823+909.4947017729\)

Price \(=\$ 1,003.7710540958\)

c. As the tenor approaches zero (maturity), the bond price decreases.

This phenomenon is called amortization of the loan.