The accounting identity assumes that anything saved is an investment, i.e. something will be done with that saving in the future. It's a bit circular, I know. It's not a lagged model, i.e. there's no explicit indexing by time of the variables, unlike (e.g.) in the Hansen–Samuelson model, which uses discrete time. There are also macroeconomic models with continuous time, e.g. Ramsey–Cass–Koopmans model.
Actually, there's a little more to be said here (as I may have committed a fallacy myself above). German economist Fabian Lindner takes issue with those (including economics textbooks authors) who use a one-good model, like Ramsey's to model financial savings:
The fallacies loanable funds theory commits might be explainable by the mis-application of some ideas and
concepts of neoclassical growth models – especially the Ramsey (1928), Solow (1956) and Diamond (1965)
models – to the sphere of money and finance. Those models are routinely taught in contemporary graduate
economics classes (Blanchard and Fischer, 1989; Romer, 1996).
The Ramsey and Solow models are models of real investment only. Financial markets, financial
assets and financial saving do not play any role in those models. There is only one good which, for simplicity,
will be called “corn”. Corn has three functions: it can be consumed, invested and used as a means of
payment since wages and interest payments are made with it. Full employment is assumed.
Without money and other financial assets, the only way units can save is to increase their tangible
assets, i.e. to invest. Given that full employment is assumed, corn production is always at its maximum in
each period. If the corn is consumed, it cannot be invested; if it is invested, it cannot be consumed. There is
thus a real trade-off between consumption and investment.
Only under this assumption does it indeed make
sense to talk about a limited saving fund which is increased when it is not consumed.
However, this trade-off between consumption and investment is not a finance constraint, but a
resource constraint. [...]
In contrast to Solow’s and Ramsey’s model, Diamond’s (1965) full employment corn economy
allows units to lend and borrow. However, they do not borrow and lend money but again the one good, corn.
They face a triple trade-off: they can eat (=consume), plant (=invest) or lend their corn. Here, consumption
are not consumption expenditures but the actual eating of the corn. When a unit wants to lend its corn, it can
of course not eat it so that it has to restrain from consumption to be able to lend it. [...]
But since in the real world money is normally not eaten or planted
and keeps circulating in the economy when it is spent or lent, those models cannot be any guide for the
analysis of a monetary economy. Specifically, what is true in a one good economy – units have to consume
less to lend and invest more – is fundamentally wrong in a monetary economy.