Question

Consider a $10k government bond due after 10 years. The bond calls for a payment of $500/year at the end of each of the next 10 years and a $10k payment at the end of the 10 years.

a) What interest rate does the bond pay?

b) 5 years go by and the bond is still trading at $10k. But there has been 5 x $500 = $2,500 in interest payments made. What is the interest rate now?

c) At the end of year 6 some and just after the 6^th interest payment has been made, the bond trades down from $10k to $9,180. What is the new interest rate on the bond?

Answer 1

Answer (a):

Bond face value = $10,000

Annual payment = $500

Interest rate =500 / 1000 = 5%

Interest rate the bond pays = 5%

Answer (b):

After 5 years since the bond is still trading at $10,000 (face value at what it was issued), the interest rate remains same.

So:

Interest rate now = 5%

Answer (c):

At the end of year 6 some and just after the 6^th interest payment has been made:

Bond price = $9,180

Remaining Time to maturity = 4 years

Annual payment = $500

Hence:

Interest rate = RATE (nper, pmt, pv, fv, type) = RATE (4, 500, -9180, 10000, 0) = 7.45%

New interest rate on the bond = 7.45%