Question

Mildred can purchase a municipal bond with a par (face) value of $1000 that will mature in 10 years. The bond pays 6% interest compounded quarterly. If she can buy this bond for $1050, what rate of return will she earn?

Answer 1

Quarterly rate of return (ROR) of bond can be computed using the following approximation formula (without using Excel):

ROR = [C + (F - P) / N] / [(F + P) / 2 where

F: Face value = $1,000

C: Quarterly bond interest (coupon) = $1,000 x 6% x (1/4) = $15

P: Bond price = $1,050

N: Number of quarters till maturity = 10 x 4 = 40

Therefore,

Quarterly ROR = [15 + (1,000 - 1,050) / 40] / [(1,000 + 1,050) / 2]

= [15 - (50 / 40)] / (2,050 / 2)

= (15 - 1.25) / 1,025

= 13.75 / 1,025

= 0.0134

= 1.34%

Annual (nominal) ROR = 1.34% x 4 = 5.36%