You purchased a $1,000 five percent coupon bond that matures in 10 years.
How much would your bond be worth if interest rates fall to 4% the day after you purchase the bond? What would the bond be worth in one year if interest rates fell to 4% at that point?
You purchased a $1,000 five percent coupon bond that matures in 10 years.
How much would your bond be worth if interest rates fall to 4% the day after you purchase the bond? What would the bond be worth in one year if interest rates fell to 4% at that point
To calculate the value of the bond, we need to use the present value formula. The formula for the present value of a bond is:
PV = C / (1 + r)^n
Where:
PV = Present Value
C = Coupon payment
r = Yield or interest rate
n = Number of periods
In this case, the bond is a $1,000 bond with a 5% coupon rate and matures in 10 years. Let's calculate the value of the bond if interest rates fall to 4% the day after you purchase the bond.
1. Calculate the coupon payment:
Coupon payment = Coupon rate * Face value
Coupon payment = 5% * $1,000 = $50
2. Calculate the present value for the new interest rate:
PV = $50 / (1 + 0.04)^10
PV = $50 / 1.04^10
PV ≈ $50 / 1.480244
PV ≈ $33.78
So, the bond would be worth approximately $33.78 if interest rates fall to 4% the day after you purchase the bond.
Now, let's calculate the bond's value in one year if interest rates fall to 4% at that point.
1. Calculate the coupon payment for one year later:
Coupon payment = 5% * $1,000 = $50
2. Calculate the present value for the new interest rate and one year:
PV = $50 / (1 + 0.04)^1
PV = $50 / 1.04
PV ≈ $48.08
So, the bond would be worth approximately $48.08 in one year if interest rates fall to 4%.