Beginning two years from now, you need to be able to withdraw $2,500,000$ shillings a year from your account to cover your Ph$.$D programme fees and other expenses payable at the beginning of each year on the programme for a period of three years. If the account pays interest at $10$ percent per annum, how much money must you have in your bank account today to meet your expenses over the university period? $($Assume no additional deposits will be made over the university period$).$

$($b$)$ Mwema Electric Company is a listed company. It increases its dividends at $5$ percent per year every year. This Utility is valued using a discount rate of $8$ percent and the shares currently sell at $85$ shillings per share. If you buy a share of this company today and plans to hold onto it for at least three years, what do you expect the value of your dividend cheque to be three years from today?

$($c$)$ An old schooldays friend has approached you regarding bond investment opportunities at the Dar es Salaam Stock Exchange $($DSE$).$ According to her, she would be comfortable to take a decision if she only knows the rate of return she would get for a one$-$year investment. From your database, there is a $15-$year bond which pays coupons annually at a coupon rate of $4$ percent and has a yield to maturity of $7\%.$ If she is interested in this bond, what rate will she earn if she buys and holds it for one year, assuming that the bond$$s yield$-$to$-$maturity, at the end of that year, will be $8\%?$