On January 1, 2020, Ellison Co. issued eight-year bonds with a face value of $5,000,000 and a stated interest rate of 8%, payable semiannually on June 30 and December 31. The bonds were sold to yield 6%. The issue price of the bonds is closest to:

Sagot :

Answer:

"$4,417,800" is the correct solution.

Explanation:

According to the question,

Principal amount,

= $5,000,000

Number of period will be:

= [tex]8\times 2[/tex]

= [tex]16[/tex]

Interest rate yield per period will be:

= [tex]\frac{8 \ percent}{2}[/tex]

= [tex]4[/tex] %

Interest rate started per period will be:

= [tex]\frac{6 \ percent}{2}[/tex]

= [tex]3[/tex] %

Now,

The present value of principal will be:

= [tex]Principal\ amount\times Yield \ discount \ factor[/tex]

= [tex]5,000,000\times 0.534[/tex]

= [tex]2,670,000[/tex] ($)

The present value of interest will be:

= [tex]Interest \ amount\times Yield \ discount \ factor[/tex]

= [tex](5,000,000\times 3 \ percent)\times 11.652[/tex]

= [tex]1,747,800[/tex] ($)

hence,

The issue price of bonds will be:

= [tex]2,670,000+1,747,800[/tex]

= [tex]4,417,800[/tex] ($)