A $3,000 bond has coupons at a rate 12% paid semi-annually and matures on December 1st, 2025 at $3,200. Find the practical clean and dirty book values of this bond on October 15th, 2020 to yield 6% convertible semi-annually.

Clean price is $3,977.22

Dirty price = $4110.99

Step-by-step explanation:

We proceed as follows;

Semiannual coupon payments = $3000* 12%/2 = 6% * 3,000 = 6/100 * 3,000 = $180

Coupons are paid on 1st June and 1st December every year(semi-annually means twice a year, every 6 months)

No. of payments remaining = 11 (1 payment in 2020 on 1st December,2020 and 2 in each of the following 5 years)

Semiannual Yield = 6%/2 =3%

The clean price of the bond is given by

P = 180/1.03+ 180/1.03^2++180/1.03^11+ 3200/1.03^11

=180/0.03*(1-1/1.03^11)+3200/1.03^11

=$3977.22

Dirty price = clean price +accrued interest

Accrued Interest = Interest from 1st June , 2020 to 1st December,2020

= no of days from 1st June to 15th October/no of days from 1st June to 1st December * $180

= 136/183*$180

=$133.77

So, Dirty price = $3977.22+$133.22 = $4110.99

what are the options? ?

step-by-step explanation:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions