You are working as a financial planner. A couple has asked you to put together an

investment plan for the education of their daughter Sophie. She is a bright seven$-$yearold $($her birthday is today$),$ a

school in $10$ years, on her $17$th birthday. You estimate that today the cost of a year of

university is $$16,000,$ including the cost of tuition, books, accommodation, food, and

clothing. You forecast that the annual inflation rate will be $3\%.$ 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 nominal interest rate is $5\%.$ 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?