Why does he use the focal date 32?

EXAMPLE 2 Nicholas deposits $2500 in a savings account today. He plans to continue mak- ing deposits every 3 months, each succeeding deposit being 2% lower than the preceding deposit. If the fund earns i(4) = 6%, how much has he accumulated at the end of 8 years, 3 months after his last deposit? We arrange the data on a time diagram below. 2500 2500(0.98) 2500(0.98) 2500(0.98)30 2500(0.98)31 Solution 0 1 2 30 31 32 S Using time 32 as the focal date, we write the equation of value for the accumulated value S of these payments at i(4) = 6%. S = 2500(1.015)32 + 2500(0.98)(1.015)31 + ... + 2500(0.98)31(1.015) The right-hand side of the equation is the sum of 32 terms of a geometric progression with t1 = 2500(1.015)32 and r = (0.98)(1.015)-1