What is the effective annual interest rate of a 20 year, $1000 principal amount, $258.40 zero-coupon bond?


Can someone please show me the steps to answering the problem or point me in the right direction? I am so lost…

A zero-coupon bond pays no interest and simply pays the principal amount at maturity. A 20-year, 00 principal amount, zero-coupon bond is currently priced at 8.40. What is the effective annual interest rate?

Posted on March 11, 2010 at 9:40 pm by admin · Permalink
In: Coupon Q&A · Tagged with: , , ,

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  1. Written by Adam
    on March 11, 2010 at 9:40 pm
    Permalink

    For a zero-coupon bond, you can think of the principal amount as the future value received (in this case, in 20 years’ time), and the present value is the current price. Since there are no coupon payments, it’s analogous to a single interest-bearing deposit that you sit there and let compound.

    So, letting the interest rate be r, and the number of years to maturity be t
    PV = 258.40
    FV = 1000.00
    r = ? (you’re wanting to find out the effective annual rate)
    t = 20

    FV = PV(1 + r) ^ t
    1000 = 258.40 * (1 + r) ^ 20
    Then, divide both sides by 258.4.

    (1 + r) ^ 20 = 1000 / 258.4
    1 + r = 20th root of (1000 / 258.4)
    1 + r = 1.0700
    r = 0.0700, or 7.00% per annum.

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