Einance A person saving for retirement puts N dollars per year in a savings account that earns interest at the rater. If S(r) is the amount of money in the account at time t, then ds constant rS+N (1) dt is the rate of change of the amount of money, measured in dollars per year. a) Solve this equation to find S(r), the total amount of money in the account at time. *Autonomous en | rs+N | = ++C =rs +N rS+N = etc ols dt ds YSTN S du Sat - dt = en/u/= ++c Y S (40) = u=vS+N en r5+N] =t+c b) Suppose the person starts saving at age 25. They put away n = 2000 dollars initially (so S(0) S=2000), and 2000 per year every year thereafter. If they get an interest rate of 8% (so r = 0.08), how much money will they have at age 65? (That is, S(40) = ?) S = ert-N du= rds dy = ds S(35) = e (-08) (40). .08 2000+C .08 S = ert-N r c) If they delay starting to save until age 30, how much will they have in their account at age 65? 65-30=35 (.08) (35) c=24794. -2000 +c 0 = 2469 3.34 +C 24693.34 = C 0 = -24794,44 +C d) If they start saving at age 25 but only get 6% interest, how much money will they have in their account at age 65? 356,149