Question

Assume that a 15-year, $1,000 face value bond pays interest of $37.50 every 3 months. If an investor requires a simple annual rate of return of 12 percent with quarterly compounding, how much should the investor be willing to pay for this bond

Answer 1

$1,249.14

Step-by-step explanation:

the effective annual rate = (1 + i)ⁿ - 1

• n = 4
• i = $37.50 / $1,000 = 3.75%

effective interest rate = 15.87%, this means that the investor should be willing to pay a premium for this bond

the effective quarterly interest required by the investor = (1 + 12%)¹/⁴ - 1 = 2.874%

market price:

PV of face value = $1,000 / (1 + 2.874%)⁶⁰ = $182.68

PV of coupon payments = $37.50 x 28.43883 (PV annuity factor, 60 periods, 2.874%) = $1,066.46

market price = $1,249.14