Suppose you purchase a zero coupon bond with a face value of $1,000, maturing in 21 years, for $212.60. Zero coupon bonds pay the investor the face value on the maturity date. What is the implicit interest in the first year of the bond's life?
You obviously understand what a zero coupon bond is.
First, we have to figure out what is the yield on the bond:
{$1,000/$212.60}^(1/21) =1.0765 - 1 x 100 =7.65% compounded annually.
The implicit interest for the 1st. year then is: 7.65/100 x $212.60 =$16.26, which is automatically added to the principal of $212.60. In this way, it compounds automatically every year @ 7.65% until maturity in 21 years, at which time your $212.60 will be worth $1,000.
+118654 Suppose you purchase a zero coupon bond with a face value of $1,000, maturing in 21 years, for $212.60. Zero coupon bonds pay the investor the face value on the maturity date. What is the implicit interest in the first year of the bond's life?
PV=212.60
FV=$1000
n=21
\(FV=PV(1+r)^n\\ 1000=212.60(1+r)^{21}\\ \frac{1000}{212.60}=(1+r)^{21}\\ \left(\frac{1000}{212.60}\right)^{1/21}=1+r\\ r=\left(\frac{1000}{212.60}\right)^{1/21}-1\\ \text{as a percent}\\ rate=100r\;\%\)
((1000/212.6)^(1/21)-1)*100 = 7.65167637374335 %
Now you want this done in EXCEL... I have done the entries but they can be changed. It will compute a different interest rate for different values :)
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