Use the following data to answer the questions:

$20-$year Treasury Yield: $3\mathrm{.}85\%$

Spread over Treasury yield on AAA Corporate Bond: $50$ bps $(0\mathrm{.}5\%)$

Spread over Treasury yield on BAA Corporate Bond: $75$ bps $(0\mathrm{.}75\%)$

$1.$ What is the price of the three bonds if they each have a coupon rate of $5\%,$ and $20$ years to maturity? Assume $$1000$ face value.

$2.$ If the Treasury yield goes up by $1\%,$ but the spreads stay the same, what will be the new prices of each bond? Did the prices increase by the same percentage?

$3.$ Suppose the yield stays at $3\mathrm{.}85\%$ and the spreads stay the same for the next year. What is the price of each bond at the end of the year?

$4.$ Continuing #$3,$ what is the return earned on each bond over the year?