Maturity Risk: All of the following bonds face the same market interest rate of

$4\%$ when they're originated and see the market interest rate increase to $6\%$ after a

year. Each has an initial present value and price of $$100,000.$ Find their first

year's rate of return.

a$)2-$year fully$-$amortized bond where the fixed payments are $$53,020$ per

year.

b$)5-$year fully$-$amortized bond where the fixed payments are $$22,463$ per

year.

c$)10-$year fully$-$amortized bond where the fixed payments are $$12,329$ per

year.

Duration Risk: All of the following bonds face the same market interest rate of

$5\%$ when they're originated and see the market interest rate increase to $10\%$ after

a year. Each has an initial price$/$present value of $$10,000.$ For each bond, find its

effective maturity when originated and its first year's rate of return.

a$)4-$year simple bond with a final payment of $$12,155$

b$)4-$year fully$-$amortized bond where the fixed payments are $$2,820$ per year

c$)4-$year coupon bond with a $$500$ annual coupon payment and a final

payment of $$10,000.$

d$)$ For each of the above, calculate the change in each bond's price using the

approximation method if the change had happened in the first year when

the bond still had $4$ years left to maturity. Compare this to the bond's

change in P based on a new PV after the interest rose to $10\%$ with $4$ years

remaining.

$\%P=-$DUR$**\frac{i}{1+i_{t-1}}$