Question

Calculate the effective annual interest rate for the following: a. A 3-month T-bill selling at $97,270 with par value $100,000. (Round your answers to 2 decimal places.) b. A 13% coupon bond selling at par and paying coupons semiannually. (Round your answers to 2 decimal places.)

Answer 1

(a) The effective annual interest rate for a 3-month T-bill selling at $97,270 with par value $100,000 is 11.71%

(b) The effective annual interest rate for a 13% coupon bond selling at par and paying coupons semiannually is 13.42%

Step-by-step explanation:

(a) A 3-month T-bill selling at $97,270 with par value $100,000

EAR =
`[par value /price]^n-1}`

n = 3 months or 12/3 = 4 times in a year

=
`[100,000/97,270]^4 - 1`

=
`[1.028066]^4 -1`

= 1.1171 - 1

= .1171 or 11.71%

b) EAR(coupon bond) =
`[1+.13/2]^2 -1`

=
`[1+.065]^2 -1`

=
`[1.065]^2 -1`

= 1.1342 - 1

= .1342 or 13.42%