Alastair has run up a credit card debt of $3000, so he decides to stop using his credit card and to pay his bank $100 a month until the debt is paid off. He figures this should take 30 months because $3000/$100 per month. Alas, he has forgotten that the bank charges interest. Suppose that the bank charges Alastair 2% interest per month.

Here's what happens each month: the bank first charges Alastair 2% interest, and then it credits his $100 payment. For example, after the first month, the bank charges Alastair $60 in interest (2% of his current debt of $3000) and then credits his $100 payment, so his debt is now $3000 + $60 â $100 = $2960.

If we let d(t) be Alastair's debt after t months, write a formula for d(t+1) in terms of dt). Please simplify your formula.