Elantra Machines forecast they will need to repair one of their machines for $$7,000$ per year

for $4$ consecutive years starting in year $7.$ To meet this obligation, they plan to invest $$x$ a

year from now and increase the investment by $5\%$ each year till the end of year $6.$ They

will then issue a purchase order to the repair company for $$7000$ each year starting in year $7$

till they finish with the maintenance schedule. If their investment attracts an interest rate of

$7\%$ per year, calculate the value of $x.$