Justin wants to accumulate $$60,000$ for a college fund over the next $15$ years for his son, Peter. Determine whether the following investment plan will allow Justin to reach his goal. Assume that compounding and payment periods are the same.

Justin plans to deposit $$200$ each month into an account that pays $5\%$ APR.

a$.$ How much money will Justin save over the next $15$ years? $

b$.$ Will Justin meet his goal? Enter yes or no$.$

c$.$ How much money is Justin over or under? $

$($Enter a positive number if he is over and a negative number if he is under$)$

d$.$ How much money did Justin deposit into the account? $

e$.$ How much total interest did Justin earn?