A U.S. savings bond was purchased at a price $95.25 per hundred. It pays interest as follows:
3% semi-annually for the first year. 4% S.A. for the second year. 5% S.A. for the third year. 6% S.A. for the fourth year. And 7% S.A. for the fifth year. What is the yield on this bond compounded semi-annually? Thanks for help.
There is NO DIRECT solution for this type of bond. However, iteration and interpolation can be used to find the Present Value of the bond that is very close to the given price of $95.25. Generally, one should try to get a PV that is lower than the given price, and another one that is higher than the given price. Then, through interpolation, one hones in to the actual price given. That rate which equates the calculated PV to the given price of $95.25 is the yield of the bond.
However, properly programmed computers and financial calculators can calculate the yield very quickly and accurately using the above procedure. So, plugging in the above numbers into the computer gives a yield of =5.99559324746% compounded semi-annually.