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

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 $6.5\%$ on the deposited tuition, and a full refund will be available if the child chooses another university. The tuition is expected to be $\$16,000$ 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 $2\%$ ? What would parents pay today if they just gave birth to a new baby and the child will attend college in 20 years? (Round to the nearest cent.)