You are working as a financial planner. A couple has asked you to put together an investment plan for the education of their daughter. She is a bright seven$-$year$-$old $($her birthday is today$),$ and everyone hopes she will go to university after high school in $10$ years, on her $17$th birthday. You estimate that today the cost of a year of university is $$11,500,$ including the cost of tuition, books, accommodation, food, and clothing. You forecast that the annual inflation rate will be $4\mathrm{.}4\%.$ You may assume that these costs are incurred at the start of each university year. A typical university program lasts $4$ years. The effective annual interest rate is $6\mathrm{.}15\%$ and is nominal.

a$.$ Suppose the couple invests money on her birthday, starting today and ending one year before she starts university. How much must they invest each year to have money to send their daughter to university? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Investment per year $

b$.$ If the couple waits $1$ year, until their daughter$$s $8$th birthday, how much more do they need to invest annually? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Additional yearly payments $