Question

A mortgage bond issued by Automation Engineering is for sale for $7,500. The bond has a face value of $10,000 with a coupon rate of 4% per year, payable monthly. What rate of return will be realized if the purchaser holds the bond to maturity 10 years from now?

Answer 1

Face value = 10000

Sale value = 7500

coupon rate = 4%

Coupon monthly payment = 0.04 * 10000 / 12 = 33.33

t = 10 * 12 = 120 months

Let return be I% per month, then

7500 = 33.33 * (P/A, I%,120) + 10000 * (P/F, I%,120)

When I = 0.5%, Value of 33.33 * (P/A, I%,120) + 10000 * (P/F, I%,120) = 8498.475

When I = 0.75%, Value of 33.33 * (P/A, I%,120) + 10000 * (P/F, I%,120) = 6710.499

I = 0.5% + (8498.475 - 7500) / (8498.475 - 6710.499) *(0.75% - 0.5%)

I = 0.5% + 0.13%

I = 0.63% ~ 0.63%

Nominal return = 0.63 * 12 = 7.6% per year (Approx)