00:01
In this problem, we need to find the premium or discount of the bond which is given to us.
00:12
We are given the par value of the bond which is equivalent to $2 ,19 ,000.
00:25
Now, we can find out the quarterly pin amount.
00:33
So, we are given the rate of interest for annual coupon amount which is equivalent to $6 ,94 ,000.
00:44
So, we simply multiply the par value of the bond times the rate of interest which is calculated and given to us times 1 divided by 4 as it is quarterly amount.
01:00
So, upon solving, we get the value as equivalent to $50 ,31 .5.
01:07
Next, we are going to find out the quarterly yield to maturity.
01:14
The value of quarterly yield to maturity will be the rate of interest which is compounded quarterly.
01:24
So, it is 9 % times 1 divided by 4.
01:29
So, we get the value as equivalent to 2 .25%.
01:33
Now, maturity period is equivalent to the bond is asked for 5 years.
01:44
Hence, we could simply multiply it 4 times to get the total number of times it is getting compounded.
01:55
So, the total factor is as follows which is equivalent to 1 minus 1 divided by 1 plus r raised to the power of n divided by r.
02:26
Here, r is the rate of interest.
02:33
So, in this case, it is 2 .25 % and the value of n is the number of years which is 20 years.
02:42
So, we could substitute the value and hence we get 1 minus 1 divided by 1 plus 2 .25 divided by 100 raised to the power of 20 divided by 2 .25 divided by 100.
03:04
So, upon solving, we get the value as equivalent to 15 .963...