Question Two a$)$ An individual has invested a sum of K $10$ m $.$ Exactly one year later, the investment is worth K$11\mathrm{.}1$m$.$ An index of prices has a value of $112$ at the beginning of the investment and $120$ at the end of the investment. The investor pays tax at $\backslash (40\backslash \%\backslash )$ on all money returns from investment. Calculate: $1.$ The money rate of return per annum before tax. $2.$ The rate of inflation. $3.$ The real rate of return per annum after tax. $[6$ Marks$]$ b$)$ A loan is repayable over $20$ years by level instalments of K$1,000$ per annum made annually in arrear. Interest is charged at the rate of $\backslash (5\backslash \%\backslash )$ per annum effective for the first $10$ years, increasing to $\backslash (7\backslash \%\backslash )$ per annum effective for the remaining term.. $1.$ Show that the amount of the original loan is K$12,033\mathrm{.}56.($Minor discrepancies due to rounding will not be penalised$).[2$ Marks$].2.$ If the level of $\backslash ($ K $1,000\backslash )$ instalments are to be replaced by the same annual payments, but with payments at the beginning of each year, calculate the revised amount of the loan. c$)$ A project gets a loan to be repaid in instalments annually in arrear. The first instalment is $50,$ the second $48$ and so on with the payments reducing by $2$ per annum until the end of the $15$ th year after which there are no further payments. The rate of interest charged by the lender is $\backslash (6\backslash \%\backslash )$ per annum effective. $1.$ Calculate the amount of the loan. $[6]2.$ Calculate the interest and capital components of the second payment.$[3$ marks$]3.$ Calculate the amount of capital repaid in the instalment at the end of the fourteenth year. $[3]$