Explanation Given: A $ 10 , 000 bond carries a coupon rate of 5.4 % . It will mature in 12 years. The current rate of interest is 6.5 % . It is assumed that the coupon rate is paid two times in a year. Formula used: I = P r t Calculation: The interest that is paid by the bond every half year is computed with the help of simple interest formula. The simple interest is computed by multiplying the principal amount by rate and time. To compute the simple interest, the principal ( P ) is $ 10 , 000 , rate of interest ( r ) is 5.4 % or 0.054 and the time ( t ) is 1 2 . The calculation is shown below: I = P r t = $ 10 , 000 × 0.054 × 1 2 = $ 270 Thus, the interest that is paid by the bond every half year is $ 270 . Now, consider the bond as a two-part investment. First part is the annuity, which pays $ 270 for next 12 years in every six months. The second part is $ 10 , 000 , which is the bond’s face value that will be paid after 12 years from now when the bond will mature. The purchaser will be willing to pay the P (present value) of both the portions of investment. Thus, assuming 6.5 % rate of interest compounded two times in a year, the rate of interest per period ( i ) is 0.065 / 2 = 0.0325 . The number of six months in 12 years is 12 × 2 = 24 , so n = 24 . Now, calculate the P (present value) of the annuity as shown below: P = R [ 1 − ( 1 + i ) − n i ] = $ 270 [ 1 − ( 1 + 0.0325 ) − 24 0.0325 ] = $ 270 [ 1 − ( 1

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 5.4, Problem 23E

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To calculate: The price that the purchaser should be willing to pay for the bond.

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Chapter 5.4, Problem 22E

Chapter 5.4, Problem 24E

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Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

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