Question

If you purchase a 5-year, zero-coupon bond for $600 (with face value of $1,000),

a) What is the yield of the bond?

b) How much could it be sold for 3 years later if the interest rates have remained stable?

c) How much would it be sold for 3 years later if the interest rates of year 4 and year 5 change to 5%?

Answer 1

Face value = $ 1000

Value of zero coupon bond = 600

Time = 5 years

a) Calculation of the Yield for Zero couon bond :-

Yield on bond = ( FV / Value of bond)^1/n - 1

= ( 1000 / 600)^1/5 - 1

Yield on bond = 1.08886688878700302 - 1

Yield on bond = 8.886688878700302%

Yield on bond = 8.89% (round off to two decimals)

b) How much could it be sold for 3 years later if the interest rates have remained stable :-

Zero coupon bond value = F / (1 + r )ⁿ

Here n = numbers year till to maturity = 5 -3 = 2 years

Here r = yield = 8.886688878700302%

Zero coupon bond value = 1000 / ( 1 + 0.08886688878700302)²

Amount you could it be sold for 3 years later if the interest rates have remained stable = $ 843.43266530174924

Amount you could it be sold for 3 years later = $ 843.43 (round off to two decimals)

c) How much would it be sold for 3 years later if the interest rates of year 4 and year 5 change to 5% :-

Zero coupon bond value = F / (1 + r )ⁿ

Here n = numbers year till to maturity = 5 -3 = 2 years

r = 5%

Zero coupon bond value = 1000 / ( 1 + 0.05)²

Amount would it be sold for 3 years later if the interest rates of year 4 and year 5 change to 5 = $ 907.02947845805

Amount would it be sold for 3 years later = $ 907.03 (round off to two decimals)