Question

You have a one-year zero-coupon bond that pays $1,000 which price today is $909.09. You have a two-year coupon bond with a principal value of $2,000 and a coupon rate of 10%. Its price is $1,845.334. Determine what is the term structure of interest rates for years 1 and 2. Draw the curve.

Answer 1

Par/Face value	1000
Annual Coupon rate	0
Annual coupon	0
Future Value = Present Value*((1+r)^t)
where r is the yield to maturity and t is the time period in years.
price of the bond = sum of present values of future cash flows
price of the bond	909.09
Use excel to find r
r	0.1
t	1
future cash flow	1000
present value	909.0909091
sum of present values	909.09
The yield to maturity for the one year bond is 10%.
Par/Face value	2000
Annual Coupon rate	0.1
Annual coupon	200
Future Value = Present Value*((1+r)^t)
where r is the yield to maturity and t is the time period in years.
price of the bond = sum of present values of future cash flows
price of the bond	1845.334
Use excel to find r
r	0.1475
t	1	2
future cash flow	200	2200
present value	174.291939	1670.772
sum of present values	1845.06
The yield to maturity for the two year bond is 14.75%.
Term Structure of interest rates.
Years to maturity	Yield to maturity
1	10%
2	14.75%

1 1 2 3 4 5 Years