The interest, once paid to the depositor, is the depositor's to keep. Banks and other financial institutions "pay" the depositor by adding the interest to the depositor's account. Unless the depositor withdraws the interest or some part of the principal, the process begins again for another interest period. Thus two interest periods (think of them as years) after the initial deposit the compound amount would be
A = P(l + r) + P(l + r)r = P{1 + r)2.