Dr$.$ Fowler has $$100,000,$ which she can put in two different types of accounts at a bank. Account A pays an interest rate of $9$ percent per year; account B pays an interest rate of $3$ percent per year plus the rate of inflation. Calculate the amount of money Dr$.$ Fowler will have at the end of one year in each account if the inflation rate is $5$ percent. What is the real rate of return in each case?