A 14-year zero-coupon bond was issued with a $1000 par value to yield 12%. What is the approximate market value of the bond?
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To calculate the approximate market value of a bond, you need to use the present value formula. The formula for present value is:
PV = FV / (1 + r)^n
Where:
PV = Present value (market value) of the bond
FV = Future value (par value) of the bond
r = Yield rate (in decimal form)
n = Number of years until maturity
In this case, the par value (FV) of the bond is $1000, the yield rate (r) is 12% (or 0.12 in decimal form), and the number of years until maturity (n) is 14.
Plugging these values into the formula, we have:
PV = $1000 / (1 + 0.12)^14
Now, let's calculate:
1 + 0.12 = 1.12
1.12^14 = 3.172207017
$1000 / 3.172207017 = $315.98 (rounded to the nearest cent)
Therefore, the approximate market value of the bond is approximately $315.98.