Your math professor has decided to retire and return to his jetsetting life style. He wishes to establish a fund from which he can withdraw $6,000 per month for the next 30 years. If the fund earns 4% per year compounded continuously, how much money does he need now to establish the fund? Exact value = dollars Rounded to the nearest cent = dollarsYour math pro'essor has decided to retire and return to his jetsetting life style. He wishes to establish a fund from which he can withdraw $5,000 per month for the next 30 years. If the fund earns 4% per year compounded continuously, how much money does he need now to establish the fund? Exact value = 1800000 [ ]_ g_l'2) dollars X Rounded to the nearest cent = 1257851342 v dollars we all know that, I = d I-en7 (r/K ) where I is invest amount d is periodic withdrawable amount N is time in year Y is continious interest rate K is number of period in a year Here we have, d= $6000 N = 30 year ,y= 4%% = 0.04 and K = year 12 month 1 month - = 12 I month .'. I = 6000 -30 (0-04) 0 .04 12 6000 = - x 12 0. 04 72000 [-e'2 ] 0. 04 = 1800 000 (1 - 2 1 2 ) so, Exact value = 1800000 (1-e-12 ) dollars ~ 1257850 . 4185 58 ~ 1257850 . 42 ( rounding to nearest cent. so, Rounded to nearest cent = 1257850. 42 dollars