At any rate, poor ol$\text{'}$ Patrick was sentenced to serve $5$ years in a federal prison and was banished from the art syndicate. During his time in prison, he decided he'd better ditch his buddy Kavis and choose a less risky, steadier career, so he took college courses ODU and became an engineer$-$GREAT CHOICE! He had to serve $5$ years in prison $(1,825$ days in all$).$ He earned forty$-$one cents per day for each of those $1,825$ days. It is now the present day and he is embarking on his new life as an engineer. He decided today to open a savings account. With his new job trying, he will be able to invest $$2,850$ annually in the account, beginning Year $1.$ He expects the account to deliver a return of $7\mathrm{.}8\%$ per year and plans to retire after accumulating $25$ years of contributions to the IRA. Assume Patrick saved up every penny he earned during his time in prison and used the sum of that savings as the initial deposit into his account. If Patrick is able to meet his goals for annual investing, about how much will he have in the retirement account after $25$ years of investment?