Qbank question on FSA

[Philly1616]

A company issued an annual-pay bond with the following characteristics:

Face value
$67,831

Maturity
4 years

Coupon
7.00%

Market interest rates
8.00%

What is the unamortized discount on the date when the bonds are issued?

A) $15,729.


B) $1,748.


C) $499.


D) $2,249.




The correct answer is D) $2,249.

The unamortized discount at the time bonds are issued will be $2,249.
Face value of bonds = $67,831
Proceeds from bond sale = $65,582 [I/Y = 8.00%, N = 4, PMT = $4,748.17 ($67,831 x 0.07 ), FV = $67,831 ]
Unamortized discount = $2,249 ($67,831 - $65,582)

Can someone explain why the FV in the calculation is 67,831 and not 100,000? Why are they even calculating the PV, isn't that already the $67,831 the face?
Thanks

 

[mwvt9]

Face value is $67,831. That is the value at which the bonds will mature (not 100,000).

So face value is the par amount for the total issue (par value=#bonds/face value).

It is unusual because we are used to seeing 1,000 par bonds all the time.