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

Answer:

(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%

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%