From Federal Reserve Economic Data $($FRED$),$ we have obtained spot zero rates as follows:

Year

Spot zero

rate

$0\mathrm{.}52\%$

$13\%$

$1\mathrm{.}5?$

$24\%$

$2\mathrm{.}5?$

$35$

We want to calculate the price of a $3-$year bond which pays $10\%$ coupon $($semi$-$annual$).$ The face value of the bond

is $$1,000.$ However, the problem is that we do not know $1\mathrm{.}5-$year and $2\mathrm{.}5-$year spot zero rates.

If we use linear interpolation method, what are the $1\mathrm{.}5-$year and $2\mathrm{.}5-$year spot zero rates?

The $1\mathrm{.}5-$year spot rate is $3\mathrm{.}50\%$ and $2\mathrm{.}5-$year spot rate is $4\mathrm{.}50\%$

The $1\mathrm{.}5-$year spot rate is $1\mathrm{.}75\%$ and $2\mathrm{.}5-$year spot rate is $2\mathrm{.}25\%$

The $1\mathrm{.}5-$year spot rate is $1\mathrm{.}70\%$ and $2\mathrm{.}5-$year spot rate is $2\mathrm{.}20\%$

The $1\mathrm{.}5-$year spot rate is $3\mathrm{.}40\%$ and $2\mathrm{.}5-$year spot rate is $4\mathrm{.}40\%$