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In: Finance

You have a one-year zero-coupon bond that pays $1,000 which price today is $909.09. You have...

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.

Solutions

Expert Solution

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


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