Present value. Prestigious University is offering a new admission and tuition payment plan for all

alumni. On the birth of a child, parents can guarantee admission to Prestigious if they pay the

first year's tuition. The university will pay an annual rate of return of $7\%$ on the deposited tuition, and a

full refund will be available if the child chooses another university. The tuition is expected to be

$$14,000$ a year at Prestigious $20$ years from now. What would parents pay today if they just gave birth

to a new baby and the child will attend college in $20$ years? How much is the required payment to

secure admission for their child if the interest rate falls to $3\%?$