Assume 6-month zero rate is 4.045%. Also use the following table to answer the questions below.
The following table gives the prices of bonds:
Face Value | Time To Maturity | Coupon / Year | Bond Price |
100 | 1 Year | 0 | 97 |
100 | 1.5 Year | 15 | 98.5 |
*Half of the stated coupon is paid every six months ** all rates are continuously compounded
What is the zero rate for 1 year?
1) 3.046%
1) 4.545%
1) 3.455%
1) 5.206%
2. What is the zero rate for 1.5 year?
2) 12.245%
2) 13.522%
2) 16.544%
2) 15.377%
a) As the One year zero coupon bond of face value 100 is priced at 97
Therefore , by the formula for price
Price = present value of all future cashflows
97 = 100 * e -(r*1)
100 = 97 *e (r*1)
er = 100/97 =1.0309
r = ln (1.0309) = 0.03046 = 3.046% (1st Option )
b) The second bond pays a coupon of 7.5 each at the end of 6 months, 1 year and 1.5 years and 100 as the redemption value at the end of 1.5 years
So , by the bond pricing formula
98.5 = 7.5 *e-(0.04045 * 0.5) + 7.5 * e-(0.03046*1) + 107.5 * e-(r*1.5)
98.5 = 7.3598 + 7.2750 + 107.5 *e-(1.5r)
=> e-(1.5r) = 83.8751/107.5 = 0.780234
=> -1.5r = ln(0.780234) =-0.24816
So r = .24816/1.5 = 0.16544 = 16.544% (3rd option)
Assume 6-month zero rate is 4.045%. Also use the following table to answer the questions below....
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