Help needed on a fixed income question

Hi, I assumed you had a typo in your original question for S1, that it should be 5.5% as I don’t seem to get your exact answers with S1=5% (an answer of 1014 instead of 1009).

Assuming that S1=5.5%, the correct answer is B, i.e. 1009.

This is derived as:

1009 = 100/[(1.055)] + 100/[(1.055)*(1.0763)] + 100/[(1.055)*(1.0763)*(1.1218)] + 1100/[(1.055)*(1.0763)*(1.1218)*(1.155)]

In your calculation (which yielded 996), you have assumed that the S4 spot rate is the same each year i.e. S1=S2=S3=S4, which is not true.

S2 = (1.055*1.0763)^(0.5)-1 = 6.56%

S3 = (1.055*1.0763*1.1218)^(1/3)-1 = 8.4%

And you already have S1 and S4. So if you discount each cashflow with their respective period’s spot rate, you’ll get the same answer, i.e. 1009 = 100/(1.055) + 100/(1.0656^2) + 100/(1.084^3) + 1100/(1.1013^4)