A zero coupon bond with a par value of 1,000 has 15 years to maturity. If the YTM is 6.2% what is the current price of this bond?
To calculate the current price of a zero coupon bond, we need to use the formula:
Current Price = Par Value / (1+YTM)^n
Where:
Par Value = $1,000
YTM = Yield to Maturity = 6.2%
n = Number of years to maturity = 15
Substituting the values into the formula, we get:
Current Price = $1,000 / (1+0.062)^15
Calculating it further:
Current Price = $1,000 / (1.062)^15
= $1,000 / 2.639946
= $378.23 (rounded to two decimal places)
Therefore, the current price of this bond is approximately $378.23.
To calculate the current price of a zero coupon bond, you would use the present value formula:
PV = F / (1 + r)^n
Where:
PV = Present value (current price) of the bond
F = Par value of the bond
r = Yield to Maturity (YTM) expressed as a decimal
n = Number of years to maturity
In this case, the par value (F) is $1,000, the YTM (r) is 6.2% or 0.062 as a decimal, and the number of years to maturity (n) is 15.
Using the formula:
PV = 1,000 / (1 + 0.062)^15
Calculating the result:
PV = 1,000 / (1.062)^15
PV ≈ 1,000 / 1.214
PV ≈ $823.43
Therefore, the current price of the zero coupon bond with a par value of $1,000 and 15 years to maturity, with a YTM of 6.2%, is approximately $823.43.