Question

A

10​-year

bond pays interest of

$28.50

​semiannually, has a face value of

$1,000​,

and is selling for

$824.70.

What are its annual coupon rate and yield to​ maturity?

Answer 1

Bond Maturity = 10 years

Semi-annual coupon = $28.50

Face Value = $1000

Bond Price = $824.70

Semi Annual Coupon Rate = Semi-annual coupon / face value = 28.5/1000 = 2.85%

Annual Coupon Rate = Semi Annual Coupon Rate * 2 = 2.85% *2 = 5.70%

Semi-annual Yield to maturity can be calculated using the RATE function in spreadsheet

RATE(number of periods, payment per period, present value, future value, when-due, rate guess)

Where, number of periods = no.of semi annual periods = 20

payment per period = semi-annual coupon = $28.50

present value = price of bond = 824.70

future value = face value = 1000

when-due = when is the payment made each semi-annual period = end = 0

rate guess = A guess value of yield to maturity = 0.1

Semi-annual Yield to maturity = RATE(20, 28.5, -824.70, 1000, 0, 0.1) = 4.1580%

This is the semi-annual yield to maturity.

Annual yield to maturity = (1+Semi-annual Yield to maturity)² -1 = (1+4.1580%)² -1 = 1.084889 -1 = 0.084889

Annual yield to maturity = 8.49%