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17 September, 12:02

A 10-year, 9.00%, $3,000 bond that pays dividends quarterly can be purchased for $2,775. This means that $2,775 is spent on the bond now. Every quarter, $67.50 is provided to the purchaser as to the dividend. After 10 years, $3,000 is given to the purchaser. If the bond is purchased and pays as scheduled, which of the following ranges of effective rate of return will the purchaser receive?

a. 10.2% - 11.2%

b. 9% - 9.5%

c. 11.21% - 13.21%

d. 9.5% - 9.95%

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  1. 17 September, 15:01
    0
    The range of effective rate of return that the purchaser will receive would be between 10.2% - 11.2%. The right answer is a

    Explanation:

    According to the given data we have the following:

    Quarterly dividend = $67.50

    Buy price = $2,775

    Maturity = 10 yrs = 10*4 = 40 quarters

    Face value = $3000

    Hence, PW = - 2775 + 67.50 * (P/A, i%,40) + 3000 * (P/F, i%,40) = 0

    67.50 * (P/A, i%,40) + 3000 * (P/F, i%,40) = 2775

    Therefore, using trail and error method

    When i = 2.5%, value of 67.50 * (P/A, i%,40) + 3000 * (P/F, i%,40) = 2811.729

    When i = 3%, value of 67.50 * (P/A, i%,40) + 3000 * (P/F, i%,40) = 2479.917

    And by using interpolation

    i = 2.5% + (2811.729-2775) / (2811.729-2479.917) * (3-2.5)

    i = 2.5% + 0.05534%

    i = 2.555%

    Nominal yeild = 2.555% * 4 = 10.22%

    Effective yeild = (1+0.02555) ^4 - 1 = 0.10618 = 10.62%

    The range of effective rate of return that the purchaser will receive would be between 10.2% - 11.2%
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