Question

Price	Maturity in years	Bond equivalent yield
400	20	?
500	20	?
500	10	?
?	10	10%
?	10	8%
400	?	8%

Fill in the table above for the zero-coupon bonds above. All of them have par values of $1,000.

Answer 1

Formula for BEY for a Zero coupon bond=

BEY=(FV/PV)^(1/n)-1

1..BEY=(1000/400)^(1/20)-1

4.69%

2..BEY=(1000/500)^(1/20)-1

3.53%

3..BEY=(1000/500)^(1/10)-1

7.18%

4..10%=(1000/PV)^(1/10)-1

0.1=(1000/PV)^(1/10)-1

Solving Algebraically,assuming Price,PV=x

ie. (1000/x)^(1/10)=1.1

(1000/x)=1.1^(1/10)

where 1.1^(1/10)=

1.009576583

So, x=

1000/1.009577=

990.51

Price=991

5..8%=(1000/PV)^(1/10)-1

0.08=(1000/PV)^(1/10)-1

Solving Algebraically,assuming Price,PV=x

ie. (1000/x)^(1/10)=1.08

(1000/x)=1.08^(1/10)

where 1.08^(1/10)=

1.007725795

So, x=

1000/1.007726=

992.33

Price=992

6..8%=(1000/400)^(1/n)-1

Solving online,

Maturity,n= 11.9 yrs.

or 12 yrs.