$$5,000$ is invested in a portfolio which is worth $$12,35012$ years and $3$ months later. What is the $12-$yr$,3-$month HPR$?$ What is the $($geometric$)$ average annual rate of return? Round to $3$ decimals: xx$.$yyy$\%$ or $.$xxyyy$2)$ An investment over $5$ years has an HPR of $-2\mathrm{.}15\%$ in the first year, $+2\mathrm{.}15\%$ in the second, $+4\mathrm{.}1\%$ in the third, $+3\mathrm{.}2\%$ in the fourth year, and $+3\mathrm{.}7\%$ in the $5$th$.$a$)$ Calculate the average annual compound rate of return over this $5-$year holding period. Round to $3$ decimals: xx$.$yyy$\%$ or $.$xxyyyb$)$ What is the simple average of the annual HPRs$?$c$)$ Suppose you had invested $$1100$ in this investment at the start. What would your investment have been worth at the end of the $2$nd year? $3)$ A portfolio starts out worth $$1500.$ After the first year, it is worth $$1612\mathrm{.}50.$ After the $2$nd$,$ its worth $$1,677\mathrm{.}00.$ After the $3$rd year, its valued at $$1,811\mathrm{.}16.$ In the $4$thyear, it earns an HPR of $-5\mathrm{.}31\%.$ a$)$ What is this portfolio worth at the end of the $4$th year?b$)$ What is its average annual rate of return?$4)$ Overall a certain holding period, a stock falls from $$85\mathrm{.}25$ to $$78\mathrm{.}75,$ and pays a dividend of $$1\mathrm{.}875.$ What is its HPR for that period? Round to xx$.$yyy$\%($or $.$xxyyy$)5)$ Calculate the monthly payment youd make on a mortgage of $$599,000$ if the $($annual$)$ interest rate is $7\mathrm{.}2\%$ and the term of the loan is $30$ years. Calculate what the payment would have been about $2$ years ago, when rates were around $3\%\mathrm{.}6)$ From the January $12,2024$ TIPS listing we used in class, find the bond that matures April $15,2032.$a$)$ What was its original coupon payment $($s$.$a$.)?$b$)$ What would the coupon payment have been as of January $12,2024?$c$)$ If the CPI on the date the bond was issued was $177\mathrm{.}50,$ what was the reference CPI value on January $12,2024($the date of the listing$)?$