Question

A zero-coupon bond, maturing in six months, has a price of $95.80 per $100 of par value. Find the six-month interest rate, in percent, rounded to two decimal places. Use continuous compounding.

		10.58%
		9.58%
		8.58%
		7.58%

Answer 1

Given,

Price = $95.80

Par value = $100

Period (n) = 6 months or 0.5 year

Solution :-

Let six-month interest rate be 'r'

Price = Par value e^(r)(n)

$95.80 = $100 e^(r)(0.5)

e^(r)(0.5) = $100 $95.80

e^(r)(0.5) = 1.043841336

Taking log both sides,

Log[e^(r)(0.5)] = Log(1.043841336)

r(0.5)[Log(e)] = 0.0429075

r(0.5) [1] = 0.0429075

r = 0.0429075 0.5

r = 0.0858 or 8.58%

Thus, the six-month interest rate is 8.58%