You deposit $1,000 at the beginning of Year 1. (a) Bank A offers you the following. Year 1: an annual nominal interest rate of 1.8% compounded monthly Year 2: a constant annual force of interest of 2% Year 3: a certain annual interest rate with a discount factor of 0.97 Solve for x, y, and z in the following time diagrams, where time is measured in years. $1,000 0 1 2 3 Sx 0 1 2 3 Sy 0 1 2 3 Sz 0 1 2 3 (b) Bank B offers an annual interest rate of i for Years 1, 2, and 3. Calculate i so that you have Sz at the end of three years