Question

2. Which security has a higher effective annual interest rate?
a. A 3-month T-bill selling at $97,645 with par value $100,000.
b. A coupon bond selling at par and paying a 10% coupon semiannually.

Answer 1

Let us first find effective annual interest rate for both options

1) A 3 month T bill selling at $ 97,645 with par value $100,000

Here T bill is for 3 months and hence ,number of compounding period = 12/3 = 4

Effective annual interest rate = (Face value/selling price)^n - 1

= (100000/97645)^4 - 1

= 1.024117978^4 - 1

= 1.100 - 1

=0.100

i.e 10%

2) Coupon bond selling at par and paying a 10% coupon semiannually.

Here number of compounding period = 2

Effective annual interest rate = (1+APR/n)^n - 1

=(1+10%/2)^2 - 1

=(1+ 5%)^2 - 1

= (1+0.05)^2 - 1

= 1.05^2 - 1

= 1.1025 - 1

=0.1025

i.e 10.25%

Thus Coupon bond selling at par and paying a 10% coupon semiannually has higher Effective annual interest rate