A firm has liabilities of $98 in one year, $100 in two years, and $107 in three years. The firm exactly matches its liabilities by purchasing the following zero or annual coupon bonds redeemable at par:

Bond Maturity Par Value Coupon Rate Effective Yield

A 1 year 100 5% 3%

B 2 years 100 0% 4%

C 3 years 100 4% 5%

Find the number of units of Bond A that must be purchased to match the liabilities exactly.

(A) 0.894

(B) 0.897

(C) 0.913

(D) 0.933

(E) 0.959