Question

If a $500 bond bearing 9.5% semi-annual coupons is purchased at 97.5 and it is redeemable at 102 in four years’ time, what is the approximate yield rate?
(8 marks)

Answer 1

Answer on question 38601 – Math - Other

If a $500 bond bearing 9.5% semi-annual coupons is purchased at 97.5 and it is redeemable at 102 in four years' time, what is the approximate yield rate?

Solution:

The approximate yield rate is:

$$R = \frac {\left[ \frac {P s - P p}{n} + I \right]}{\left[ \frac {P s + P p}{2} \right]},$$

Where Ps - selling price of bonds; Pp - the purchase price of the bonds, and n - the number of years of tenure a bond; I - annual interest income.

$$I = 5 0 0 * 0. 0 9 5 * 2 = \$ 9 5$$ $$R = \frac {\left[ \frac {1 0 2 - 9 7 . 5}{4} + 9 5 \right]}{\left[ \frac {1 0 2 + 9 7 . 5}{2} \right]} = 96.36\%.$$