Use the following information to answer the remaining questions.

Suppose you observe the following securities$.$ Assume that all of them are priced correctly based on the appropriate spot rates.

$1-$year STRIP with a par value of $$100$ and a price of $$97($assume annual compounding$)$

$2-$year STRIP with a par value of $$100$ and a price of $$91($assume annual compounding$)$

Treasury bond priced at par with $3$ years left to maturity, a $5\%$ coupon, and a $$1000$ par value $($assume coupons are paid annually$)$

Treasury bond priced at par with $4$ years left to

maturity, a $6\%$ coupon, and a $$1000$ par value $($assume coupons are paid annually$)$

Calculate the $1-$year spot rate. $($Correct answer: $0\mathrm{.}0309)$

Calculate the $2-$year spot rate. $($Correct answer: $0\mathrm{.}048)$

Calculate the $3-$year spot rate. $($Correct answer: $0\mathrm{.}0498$

Calculate the $4-$year spot rate. $($Correct answer: $0\mathrm{.}0612)$

Suppose you observe a $3-$year Treasury bond with a $2\%$ coupon $($paid annually$)$ and a $$1,000$ par value. What is the arbitrage$-$free price of this bond? $($Correct answer: $919\mathrm{.}7)$

Suppose you observe a $4-$year Treasury bond with a $3\%$ coupon $($paid annually$)$ and a $$1,000$ par value. What is the arbitrage$-$free price of this bond? $($Correct answer: $894\mathrm{.}52)$

Suppose that the bond in question #$7$ has a yield$-$to$-$maturity of $5\mathrm{.}50\%.$ If you were to exploit this mispricing opportunity, what would your arbitrage profit be$?($Correct answer: $17\mathrm{.}85)$

Assume that you can invest any amount in STRIPS and that $1-4-$year STRIPS are correctly priced based on the spot rates that you have calculated. In order to benefit from the arbitrage opportunity in question #$8,$ how much should you invest in a $1-$year STRIP?

Assume that you can invest any amount in STRIPS and that $1-4-$year STRIPS are correctly priced based on the spot rates that you have calculated. In order to benefit from the arbitrage opportunity in question #$8,$ how much should you invest in a $2-$year STRIP?

Assume that you can invest any amount in STRIPS and that $1-4-$year STRIPS are correctly priced based on the spot rates that you have calculated. In order to benefit from the arbitrage opportunity in question #$8,$ how much should you invest in a $3-$year STRIP?

Assume that you can invest any amount in STRIPS and that $1-4-$year STRIPS are correctly priced based on the spot rates that you have calculated. In order to benefit from the arbitrage opportunity in question #$8,$ how much should you invest in a $4-$year STRIP?