Calculate the theoretical value of a 3-years 5 coupon bond under the assumption that the market interest rate is 46

To calculate the theoretical value of the bond, we need to use the formula for the present value of a bond:

PV = C/(1+i)^1 + C/(1+i)^2 + C/(1+i)^3 + ... + C/(1+i)^n + F/(1+i)^n

Where: PV = present value of the bond C = coupon payment i = market interest rate n = number of years until maturity F = face value of the bond

In this case, we have:

C = 5% x $1000 = $50 (since the coupon rate is 5% and the face value is $1000) i = 4.6% n = 3 years F = $1000

Using these values in the formula, we get:

PV = $50/(1+0.046)^1 + $50/(1+0.046)^2 + $50/(1+0.046)^3 + $1000/(1+0.046)^3 PV = $50/1.046 + $50/1.095 + $50/1.144 + $1000/1.144 PV = $47.87 + $45.67 + $43.54 + $788.85 PV = $925.93

Therefore, the theoretical value of the bond is $925.93