A financial institution accepts a $20,000 deposit from a customer on which it guarantees to pay…

A financial institution accepts a $20,000 deposit from a customer on which it guarantees to pay 10% effective for two years. The customer ex- presses an intention to withdraw half the proceeds at the end of the first year. The financial institution can invest in either one-year zero coupon bonds yielding 10% or two-year zero coupon bonds yielding 11%. The insti- tution is analyzing two options: A- An absolute matching strategy, where each liability is paired with an asset of the same future value on the same date, B- Investing entirely in two-year bonds to receive the higher rate. (a) Find the profit at inception to the institution under Option A. (b) Find the one-year forward rate on one-year bonds at which Option B would be equivalent to Option A.