The prices of zero-coupon bonds with various maturities are given in the following table.

Suppose that you want to construct a 2-year maturity forward loan commencing in 3 years. The face value of each bond is $1,000.

Maturity (Years)	Price
1	$	963.43
2		890.89
3		827.92
4		766.00
5		690.68

a. Suppose that you buy today one 3-year maturity zero-coupon bond. How many 5-year maturity zeros would you have to sell to make your initial cash flow equal to zero? (Round your answer to 4 decimal places.)

b. What are the cash flows on this strategy in each year? (Negative value should be indicated by a minus sign. Leave cell blank if there is no effect. Round your answers to 2 decimal places.)

c. What is the effective 2-year interest rate on the effective 3-year-ahead forward loan? (Round your answer to 2 decimal places.)

d. Confirm that the effective 2-year forward interest rate equals (1 + f₄) (1 + f₅) 1. You therefore can interpret the 2-year loan rate as a 2-year forward rate for the last two years. Alternatively, show that the effective 2-year forward rate equals (Round your answer to 2 decimal places.)

(1 + y5)5	- 1
(1 + y3)3