Question

An investor purchases a zero coupon bond with 12 years to maturity at a price of $565.66. The bond has a par value of $1,000. What is the implicit interest for the first year? Assume semiannual compounding.

Answer 1

Interest earned per half year = CAGR

CAGR = (End Value /Starting Value)^{1/number of periods}

Where, end value = 1000, starting value = 565.66, number of periods = number of years × 2 = 12 × 2 = 24

Therefore, CAGR = (1000/565.66)^1/24 -1 = (1.7678464)^1/24 -1 = 1.024 -1 = 0.024 = 2.4%

Therefore, Interest Rate per half year = 2.4%

Therefore, Implicit Interest Rate for 1st year = (1+i)ⁿ - 1

Where, i = interest rate = 0.024 and n = number of periods i.e. half years = 2

Therefore, Implicit Interest Rate = (1+0.024)² - 1 = 1.048576 - 1 = 0.048576 = 4.8576%

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