Question

1
Two annuities and two zero coupon bonds are available to buy or sell today. Their characteristics are: • The first annuity, A1, makes payments of $1000 twice per year for 5 years. The price of this annuity is $8743.37. • The second annuity, A2, makes payments of $100 twice per year for 2 years. This annuity has an internal rate of return of Rj = 4.36%. • The first zero coupon bond, Z1, has face value $10,000, and maturity 5 years. The price of this bond is $7667.85. . The second zero coupon bond, Z2, has face value $10,000 and maturity 2 years. The price of this bond is $9104.95.

Answer 1

For A1, to calculate the forward price of this annuity we have to first calculate the interest rate

Using this formula,

1-(1+i)-n PV = C*

PV= $8743.27 C= $2000 and n =5

i = 4.65%

Now at Time(T)= 2, we will have to calculate the FV of the bond using this formula,

FV =C+(1+i)" - 1

But in this case, n= 3 years since 2 years have passed

FV = 2000 * 3.1417 = 6283.32

Hence, the forward price to buy the annuity A1 would be $6283.32