Question

Which security has a higher effective annual interest rate?

(a) A four-month T-bill selling at $96.5 with face value of $100.

(b) A three-year coupon bond selling at $98 and paying a 10% coupon semi-annually.

Answer 1

A four-month T-bill selling at $96.5 with face value of $100.

Effective annual rate = (FV/MV)^12/n - 1 = (100 / 96.5)^12/4 - 1 = 11.28%

A three-year coupon bond selling at $98 and paying a 10% coupon semi-annually.

Semi annual yield = Rate (Nper, PMT, PV, FV) = Rate (2 x 3, 10%/2 x 100, -98, 100) = 5.40%

Hence, the effective annual interest rate = (1 + semi annual yield)² - 1 = (1 + 5.40%)² - 1 = 11.09%

Hence, the four-month T-bill has a higher effective annual interest rate.