Some friends of yours have just had a child. Thinking ahead, and realizing the power of compound interest, they afe considering investing for their child's college education, which will begin in $18$ years. Assume that the cost of a college education today is $$150,000.$ Also assume there is no inflation and no tax on interest income used to pay college tuition and expenses.

Instructions: Enter your responses rounded to the nearest dollar. Do not round intermediate calculations.

a$.$ If the interest rate is $5$ percent, how much money will your friends need to put into their savings account today to have $$150,000$ in $18$ years?

They would need to put $ into their savings account today.

b$.$ What if the interest rate were $7$ percent?

They would need to put $ into their savings account today.

c$.$ The chance that the price of a college education will be the same $18$ years from now as it is today seems remote. Assuming that the price will rise $4$ percent per year, and that today's interest rate is $8$ percent, what will your friends' investment need to be$?$

The amount of the investment would be $

d$.$ Return to the case with a $5$ percent interest rate and no inflation $($part a$).$ Assume that your friends don't have enough financial resources to make the entire investment at the beginning. Instead, they think they will be able to split their investment into two equal parts, one invested immediately and the second invested in $5$ years. What is the amount of each part?