$5\mathrm{.}22$ Repeat Problem $2\mathrm{.}32$ for continuous compounding at $84\%.$ How significant is the $\%$ difference vis$-$a$-$vis Problem $5\mathrm{.}21?$ Ans. $$177478\mathrm{.}942\mathrm{.}32$ Ms$.$ Frank is planning for a $25-$year retirement period and wishes to withdraw a portion of her savings at the end of each year. She plans to withdraw $$10000$ at the end of the first year, and then to increase the amount of the withdrawal by $$1000$ each year, to offset inflation. How much money should she have in her savings account at the start of the retirement period, if the bank pays $($a$)9\%,($b$)7\%,$ per year, compounded annually? Ans.$($a$)$ $$175152\mathrm{.}28$; $($b$)$ $$205435\mathrm{.}72$