A one-year zero-coupon bond yields 4.0%. The two and three year zero coupon bond

Question

A one-year zero-coupon bond yields 4.0%. The two and three year zero coupon bonds yield 5.0% and 6.0% respectively. (please show work, so I can learn)

1.The rate for a one year loan beginning in one year is closest to:

2. The forward rate for a two year loan beginning in one year is closest to:

3. The forward rate for a one year loan beginning in two years is closest to:

4. The five year spot rate is not given however, the forward price for a two-year zero coupon bond beginning in three years is known to be 0.8479. The price today of a five year zero-coupon bond is closest to:

Explanation / Answer

1. one year rate = 0.04 and 2 year rate = 0.05

Hence,the rate for a one year loan beginning in one year is closest to = (1+0.04)*(1+r) =(1.05)^2

(1+r) = (1.05)^2/(1.04) = 1.0601

Hence the  rate for a one year loan beginning in one year is closest to 6.01%

2. Here (1.04)*(1+r)^2 = (1+0.06)^3

(1+r)^2 = (1.06)^3/1.04

1+r = ((1.06)^3/1.04 )^(1/2)

r = 7,014% or 7.01%

3. Here, (1.04)*(1.05)*(1+r) = (1.06)^3

(1+r) = (1.06)^3/(1.04*1.05)

r = 0.09067 = 9.07%

4. The five year rate of a zero-coupon bond =(((1+0.06)^3 *(1+ 0.08479)^2)^(1/5) -1)= (((1.06)^3 *(1.08479)^2)^(1/5)-1) = (1.069847 - 1) = 0.06984 = 6.98%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.