Question

Lionel purchased a $5,000 bond that was paying a coupon rate of 4.40% compounded semi-annually and had 8 more years to mature. The yield at the time of purchase was 5.80% compounded semi-annually.

a. How much did Lionel pay for the bond?

Round to the nearest cent

b. What was the amount of premium or discount on the bond?

(click to select)Premium or Discount

amount was ____

Round to the nearest cent

Answer 1

Price of Bond = C * [( 1 - ( 1 + R)^-N) / R] + FV / ( 1 + R)^N

Where, C = Coupon Payment

R = Yield Per period

N = Number of periods till maturity

FV = Face value

Yield Per period ( Semi - Annually) = 5.80% / 2

= 2.90%

Coupon Payment = Face value * Coupon rate * ( 1 / Number of compounding)

= 5000 * 4.40% * ( 1 / 2)

= 110

Number of Periods = 8 * 2

= 16

Price of bond = 110 * [( 1 - ( 1 + 2.90%)^-16] / 2.90% + 5000 / ( 1 + 2.90%)^16

= 110 * [( 1 - (1.0290)^-16] / 0.0290 + [5000 / (1.0290)^16]

= 110 [( 1 - 0.63292755) / 0.0290] + [5000 / 1.57995965]

= 110 *12.65767 + 3164.6377

= 4556.98  [ rounded to two decimals]

A) Price of bond is 4556.98

B) Bond is trading at discount

= 5000 - 4556.98

= 443.02