another derivative question

[archived_user]

A 4 percent Treasury bond has 2.5 years to maturity. Spot rates are as follows:
6 month
1 year
1.5 years
2 years
2.5 years
2%
2.5%
3%
4%
6%
The note is currently selling for $976. Determine the arbitrage profit, if any, that is possible.
A) $19.22.
B) $43.22.
C) no profit is possible as the present value of expected cash flows equals the current market price.
D) $37.63.
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The answer is A. But I still don’t understand the explanation given by schweser. Could someone please elaborate? Thanks,

 

[archived_user]

20/(1.01^1)
20/(1.0125^2)
20/(1.015^3)
20/(1.02^4)
1020/(1.03^5)
sum=956.77
976-956.77=19.22
Think of each payment coupon and principal as a series of zero coupon at the rate described. so 4 series of zero coupons at 20$ discounted at it’s respective rate and 1020$ at the 2.5 year rate should equal the cost of the bond, else there will be arbitrage opportunities

 

[archived_user]

Thank you so much xck2000. That makes much more sense. The payments are discounted semi-annually. As long as I can figure out what the price should be. I can determine the actual arbitrage amount given the actual price in the market. Thanks again