Question

Q1: Assume that coupons are paid semi-annually as in the US Government bond market:

Bond A: has a coupon rate of 7% and matures in 3.5 years to maturity. What is the price of this bond if its yield to maturity is 5%?

Bond B: costs $950 dollars and matures in 15 years. The yield to maturity (YTM) on this bond is 4%.

1)What is the semiannual coupon payment of this bond (in dollars)?

2) What is its annual coupon rate?

3)What is the yield to maturity on 2-year Bond C if its price is $998 and the coupon rate is 1.5%?

Q2:

1)What effective annual rate results from continuous compounding of 8%?

2) Suppose that the effective annual rate under continuous compounding is 10%. What is the simple rate (without effects of compounding included)?

Answer 1

Bond A:

Assuming the face value to be $1,000

Coupon payment = 0.07 * 1000 = 70 / 2 = 35 ( since it is a semi annual bond, we divide by 2)

Number of periods = 3.5 * 2 = 7

Yield to maturity = 0.05 / 2 = 0.025 or 2.5%

Bond price = 35 * [ 1 - 1 / ( 1 + 0.025)⁷] / 0.025 + 1000 / ( 1 + 0.025)⁷

Bond price = 35 * 6.349391 + 841.265235

Bond A price = $1,063.494

Bond B:

Number of periods = 15 * 2 = 30

Yield to maturity = 0.04 / 2 = 0.02 or 2%

950 = Coupon * [ 1 - 1 / ( 1 + 0.02)³⁰] / 0.02 + 1000/ ( 1 + 0.02)³⁰

950 = Coupon * 22.396456 + 552.070889

397.929111 = Coupon * 22.396456

17.77 = Coupon

Semi- annual coupon is $17.77

Annual coupon = 17.77 * 2 = 35.54

Annual coupn rate = (35.54 / 1000) * 100

Annual coupn rate =3.554%

Bond C:

I am assuming the coupon are paid manuaaly as the question does not metion semi-annual

face value = 1000

Coupon payment = 0.015 * 1000 = 15

Price = 998

Number of periods = 2

Yield to maturity using a financial calculator = 16.02%

Keys to use in the calculator: PV = -998, FV = 1000, PMT = 15, N = 2, CPT I/Y

Questio 2:

Continous compunding of 8%

e^0.08 - 1 = 0.083287 or 8.3287%

e^x - 1 = 0.1

e^x = 1.1

X = LN 1.1

X = 0.09531 or 9.531%