what price should you pay for a $ 2000 face value,5 year bond which has $ 100 half yearly coupons, assuming that you want a 4% p.a yield,compounded semiannually?
To calculate the price you should pay for the bond, we need to use the present value formula for a bond. The present value of a bond is the summation of the present value of its coupon payments and the present value of its face value.
The formula for the present value of a bond is as follows:
PV = (C / (1 + r/n)) + (C / (1 + r/n)^2) + ... + (C / (1 + r/n)^n) + (F / (1 + r/n)^n)
Where:
PV = Present value of the bond
C = Coupon payment
r = Yield rate
n = Number of coupon periods per year
F = Face value of the bond
In this case:
Coupon payment (C) = $100
Yield rate (r) = 4% p.a (compounded semiannually) = 2% per half-year
Number of coupon periods per year (n) = 2
Face value (F) = $2000
Plugging these values into the formula, we can calculate the present value of the bond:
PV = (100 / (1 + 0.02/2)) + (100 / (1 + 0.02/2)^2) + (100 / (1 + 0.02/2)^3) + (100 / (1 + 0.02/2)^4) + (100 / (1 + 0.02/2)^5) + (2000 / (1 + 0.02/2)^5)
Now, calculate the present value using this formula.