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 $$10,500,$ including the cost of tuition, books, accommodation,

food, and clothing. You forecast that the annual inflation rate will be $4\mathrm{.}2\%.$ 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

$6\mathrm{.}05\%$ 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 $