Question

A 25-year bond is currently selling for $452.32. It has a face value of $1,000. Its coupon rate is 4%, paid semiannually. What is this bond’s yield to maturity?

a)5.00%

b)4.00%

c)8.84%

d)10.06%

e)10.00%

Answer 1

Option (c) is correct

The formula for yield to maturity is:

Yield to maturity = C + F - P /n / F + P / 2

where, C is the coupon payment, F is the face or par value of the bond = $1000, P is the current price of the bond = $452.32 and n is the no. of years to maturity = 25.

Coupon payments = $1000 * 4% = $40

Putting the values in the above formula, we get,

Yield to maturity = $40 + ($1000 - $452.32) / 25 / ($1000 + $452.32) / 2

Yield to maturity = $40 + ($547.68 / 25) / ($1452.32 /2)

Yield to maturity = $40 + 21.9072 / $726.16

Yield to maturity = $61.9072 / $726.16

Yield to maturity = 8.53% approx.

Approx answer is 8.53%. So, we can take 8.84% as yield to maturity.