Please help.
Which investment is better?:
1) A US treasury bond with 3% coupon paid semi-annually and is priced @ $90.00 per hundred and matures in exactly 5 years.
2) A US savings bond that also matures in 5 years and is priced at $100.00 and pays semi-annual interest as follows: 1st. year: 3%, 2nd. year: 4%, 3rd. year: 5%, 4th. year: 6%, and 5th. year: 9%. Thanks for any help.
Which is the better investment?. In reality, it means which investment has a greater yield.
1) Bond yields cannot be solved directly, but only through iterations. My computer has this formula programmed in it and can solve for any variable:
1.5*[(1-(1+R)^-10)/(R)]+100*(1+(R))^-10-90=0, solve for R,
R=2.65155365262 per 1/2 year. Multiply it by 2 to get annual rate:
R=5.30310730524% compounded semi-annually.
2) The second bond's yield is found through "Cash Flow Analysis" Even though, the same as the first bond, there is no direct solution, again iterations can be used to find the yield, which is called "IRR", or Internal Rate of Return. This common formula is used: PV=FV[1 + R]^-N. The PV of all the payments plus the PV of the par value is calculated until it equates to the purchase price of $100. Again, this formula is programmed into my computer and can do many iteration per second. As a result, it found
R=2.62798318041 per 1/2 year. Multiply it by 2 to get annual rate.
R=5.25596636082% compounded semi-annually.
As can easily be seen, there isn't that much difference between the two bonds. The first bond has a slightly higher yield.
