JUST NEED THE ANSWER TO C$,$ but correct anything wrong in the other questions

$1.(30)$ Go to the U$.$S$.$ Treasury website here and look up the daily yield curve rates. Note that the rates are reported as percentages, so $0\mathrm{.}35$ should be read as $0\mathrm{.}35\%$ or r $=0\mathrm{.}0035.$

$($a$)(10)$ Report the yields for the one, two, and three$-$year Treasury notes. Is the yield curve upward or downward sloping? According to the expectations theory, what does this say about investors$$ beliefs regarding short term interest rates?

$1/28/25$

$1$yr $=4\mathrm{.}14\%$

$2$yr $=4\mathrm{.}19\%$

$3$yr $=4\mathrm{.}25\%$

The yield curve is upward sloping because the yield rates are increasing as the maturity years increase. Long term bonds usually offer higher yields than short term bonds to make up for the added risk over the longer time period. According to the expectations theory, the shape of the yield curve reflects expectations for short term interest rates. Since the curve is upward sloping, investors expect long term rates to be higher than short term rates, aka short term rates will rise in the future. The market in this case expects short term rates to rise from $4\mathrm{.}14\%.$

$($b$)(10)$ Although we cannot know what future bond yields will be$,$ we can look back in time and check whether investors$$ past beliefs were confirmed. Report the historical yields for the same Treasury notes from dates one, two, and three years ago. Do the expectations indicated by the historical yield curves line up with the actual movement of interest rates?

One year ago $1/29/24($downward sloping$/$inverted$)$

$1$yr $=4\mathrm{.}76\%$

$2$yr $=4\mathrm{.}29\%$

$3$yr $=4\mathrm{.}10\%$

Two years ago $1/27/23($downward sloping$/$inverted$)$

$1$yr $=4\mathrm{.}68\%$

$2$yr $=4\mathrm{.}19\%$

$3$yr $=3\mathrm{.}90\%$

Three years ago $1/28/22($upward sloping$)$

$1$yr $=0\mathrm{.}75\%$

$2$yr $=1\mathrm{.}15\%$

$3$yr $=1\mathrm{.}38\%$

The expectations indicated by the historical yield curves usually line up with the actual movement of interest rates. Specifically, in $2022,$ the upward sloping yield curve correctly predicted rates would rise, as the Fed raised rates to address inflation. In $2023$ and $2024,$ the curves were downward sloping, so investors expected short term rates to decrease in the future. However, that was incorrect, and those curves did not align well with actual movement of interest rates.

$($c$)(10)$ For each of the previous years, use the one and two$-$year spot rates to calculate the one$-$year forward rate one year from that date and check how it compares to the actual one$-$year spot rate from the following year.

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