Your younger brother has come to you for advice. He is about to enter college and has two options open to him. His first option is to study engineering. If he does this, his undergraduate degree would cost him $$12,000$ a year for $4$ years. Having obtained this, he would need $2$ years of practical experience; in the first year he would earn $$20,000,$ in the second year he wold earn $$25,000.$ He then would need to obtain is master's degree, which will cost $$25,000$ a year for $2$ years. After that he will be fully qualified and can earn $$40,000$ per year for $25$ years. His other option is to study accounting. If he does this, he would pay $$13,000$ a year for $4$ years and then he would earn $$31,000$ per year for $30$ years. The effort involved in the two careers is the same, so he is only interested in earnings the jobs provide. What advice would you give him if the applicable interest rate is $5\%?$ A day later he comes back and says he took your advice $,$ but in fact, the applicable interest rate was $6\%.$ Has your brother made the right choice?