Calculate and provide answer for the following questions.

$($a$)$ Your employer has promised to give you a $$5,000$ bonus after you have been working for him for $5$ years. What is the present value of this bonus if the proper discount rate is $8\%?$

$($b$)$ You decide to put $$10,000$ in a money market fund that pays interest at the annual rate of $7\mathrm{.}2\%,$ compounding it monthly. You plan to take the money out after one year. Find the total amount available to you.

$($c$)$ Alpha Ltd has just paid a dividend per share of $ $1\mathrm{.}30.$ Shares are valued only on the basis of expected dividends. An annual sustainable growth of dividends of $3\%$ is assumed. The appropriate discount rate is $10\%$ per year. Compute the share value.

$($d$)$ A company buys a piece of equipment for $2$ million on January $1.$ The expected useful life is $6$ years and the salvage value is estimated zero. The company intends to replace the equipment identically. The average expected price increase is $8\%$ yearly. For this purpose, the company creates a special fund with annual equal payments at the end of each year during the lifetime. Cost of capital and earnings of the fund is $10\%$ per year. Compute the annual payment into the fund.