Problem solving: Show your solutions, please. Round off final answers to two decimal places. Label all your numbers, example nper $($number of periods$)=5.$ Use excels for your solutions. Highlight final answer.

$1.$ Determine the equilibrium price of the security given the following information. What is quantity demanded and quantity supplied?

Quantity demanded: BD$=1,350-\mathrm{.}30$p

Quantity supplied: BS$=1,200+\mathrm{.}12$p

$2.$ Suppose you buy a $10-$year bond today for $$980\mathrm{.}00$ and that the coupon rate is $8\%$ paid semi$-$annually. After a year, the market interest rate decreases to $6\%,$ determine: a$)$ bond price; b$)$ rate of return for the bond.

$3.$ Which will you prefer to invest your $$1,500$: a$)$ a two$-$year bond with interest rate of $10\%$ or b$)$ two one$-$year bonds, Year $1,$ the bond will earn $9\%$ and year $2$ the second bond will earn $10\%.$ Which bond will you buy?

$4.$ Suppose that the interest rate on a one$-$year bond is $3\mathrm{.}25\%$ today and interest rates expected on one$-$year bonds in the future are $3\mathrm{.}85\%$ in one year, $4\mathrm{.}25\%$ in two years and $5\mathrm{.}1\%$ in three years

$4\mathrm{.}1.$ According to the expectations theory of the term structure, what are the interest rates today on a$)$ a two$-$year bond; b$)$ a three$-$year bond and c$)$ a four$-$year bond?

$4\mathrm{.}2.$ If the term premium is equal to $0\mathrm{.}75$ percent, what are the interest rates today for a $1)$ two$-$year bond, $2)$ three$-$year bond; $3)$ four$-$year bond.

$5.$ If the expected real interest rate is $8\%,$ expected inflation rate is $3\%,$ determine the nominal interest rate and after$-$tax expected real interest rate. Tax rate is $25\%.$

$6.$ Determine the following:

$6\mathrm{.}1.$ Herfindahl$-$Hirschman index $($HHI$)$ with the following information of the six banks$$ deposits;

$6\mathrm{.}2.$ If the biggest and smallest bank $($in terms of deposits$)$ merge, what will be the HHI for all the remaining banks?

$6\mathrm{.}3.$ Will the merger be allowed?