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%

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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