Some friends of yours have just had a child. Thinking ahead, and realizing the power of compound interest, they are considering investing for their child$$s college education, which will begin in $18$ years. Assume that the cost of a college education today is $$125,000.$ Also assume that there is no inflation and there are no taxes on interest income that is used to pay college tuition and expenses.

A$.)$ If the annual effective interest rate is $6\%,$ how much money will your friends need to put into their savings account today to have $$125,000$ in $18$ years?

B$.)$ 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 $3\%$ per year, and that today$$s interest rate is $6\%,$ what will your friends$$ investment need to be$?$

C$.)$Return to part a$,$ the case with a $6\%$ annual effective interest rate and no inflation. Assume that your friends don$$t have enough financial resources to make the entire investment at the beginning. Instead, they would like to make monthly contributions. How much do they need to contribute monthly to have $$125,000$ in $18$ years? Use a monthly interest rate of $0\mathrm{.}49\%$