A "zero coupon bond" (or just "zero") is a bond, that does not pay any interest, it just pays the face value when it matures. Of course nobody would purchase a bond without interest, that's why zero coupon bonds are sold at a discount.
Suppose you are given the following information about the current prices of zero coupon bonds:
bond: |
price |
1-year zero, face value $1,000 |
$909.09 |
2-year zero, face value $1,000 |
$826.45 |
3-year zero, face value $1,000 |
$718.65 |
I.e. if you buy 1-year zero, you must pay now $909.09 and you will receive $1,000 as the bond matures in exactly 1 year, or, alternatively, if you buy 3-year zero, you pay today $718.65 and will receive $1,000 in exactly 3 years.
Given the information, find:
Answer: We will use the financial calculator to calculate the below answers
1. Yields to maturity for each bond
1. N = 1, PV = $909.09, FV = $1,000, PMT = 0 and I/Y = 10.00011%
2. N = 2, PV = $826.45, FV = $1,000, PMT = 0 and I/Y = 9.99%
3. N = 3, PV = $718.65, FV = $1,000, PMT = 0 and I/Y = 11.642%
2. what is the price of 3-year coupon bond, if the coupon payment is $100 ($100 received at the end of each year 1, 2, and 3)?
N = 3
PMT = $100
I/Y = 11.642%
FV = $1000
PV = $960.32
3. Given the price of 3-year coupon bond calculated above and coupon payment of $100 at the end of each year 1, 2, and 3, calculate coupon bond rate.
Coupon bond rate = Coupon/Face value
Coupon bond rate = 100/1000
Coupon bond rate = 10%
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