ScanSoft, the new company Hassan is going to work for, is developing a new process to

manufacture optical disks. The development costs were higher than expected, so ScanSoft

requires an immediate cash inflow of $$5,200,000.$ To raise the required capital, the company

decided to issue bonds. Since ScanSoft had no expertise in issuing and selling bonds, Hassan

suggested that the company work with an investment dealer. The investment dealer bought

the company's entire bond issue at a discount, and then planned to sell the bonds to the public

at face value or the current market value. To ensure it would raise the $$5,200,000$ it required,

ScanSoft plans to issue $5200$ bonds with a face value of $$1000$ each, on January $20,2024.$

Interest is paid semi$-$annually on July $20$ and January $20,$ beginning July $20,2024.$ The bonds pay

interest at $5\mathrm{.}5\%$ compounded semi$-$annually.

Hassan Mustafa realized that when the bonds mature on January $20,2044,$ there must be

$$5,200,000$ available to repay the bondholders. To have enough money on hand to meet this

obligation, He suggested that ScanSoft set up a sinking fund $($an interest$-$bearing account into

which payments are made at regular intervals to provide a desired sum of money at a specified

future time$)$ using a specially designated savings account. The company earns interest of $1\mathrm{.}6\%$

compounded semi$-$annually on this sinking fund account. ScanSoft began making semi$-$annual

payments to the sinking fund on July $20,2024.$

ScanSoft issued the bonds, sold them all to the investment dealer, and used the money raised

to continue its research and development.

$1.$ How much would an investor have to pay for one of these bonds to earn $4\mathrm{.}4\%$

compounded semi$-$annually?

$2.$

a$.$ What is the size of the sinking fund payments?

b$.$ What will be the total amount deposited into the sinking fund account would be by

January $2044?$

c$.$ How much of the sinking fund will be interest?

$3.$ Suppose ScanSoft discovers on January $20,2034,$ that it can earn $2\mathrm{.}5\%$ interest

compounded semi$-$annually on its sinking fund account.

a$.$ What is the balance in the sinking fund after the January $20,2034,$ sinking fund

payment?

b$.$ What is the new sinking fund payment if the fund begins to earn $2\mathrm{.}5\%$ on January $21,$

$2034?$

c$.$ What will be the total amount deposited into the sinking fund account the life of the

bonds?

d$.$ How much of the sinking fund will then be interest?

Note: Please provide the answer step by step in detail by using formulas and proper calculations. I don't want my answers to be solved by Excel or in the form of table charts. Thank you...