Suppose that you discover in your attic an overdue library book on which your grandfather owed a fine of 30 cents 100 years ago. if an overdue fine grows exponentially at a 5% annual rate compounded continuously, how much would you have to pay if you returned the book today? (hint: if a(t) is the balance at the time t, then , where r is the interest rate expressed as a decimal, not in the percentage form).
FV=P*e^rt, where FV is future value, P is the principal, r is the interest rate, and t is the time. So in this case, we have: FV=.30*e^100*0.05=.3*e^5=$44.524 due in fines, or 148 times the original 30-cent fine ☺☺☺☺
