The most common forms of debt are loans, including mortgages and auto loans, and credit card debt. Under the terms of a loan, the borrower is required to repay the balance of the loan by a certain date, typically several years in the future. The terms of the loan also stipulate the amount of interest that the borrower is required to pay annually, expressed as a percentage of the loan amount. Interest is used as a way to ensure that the lender is compensated for taking on the risk of the loan while also encouraging the borrower to repay the loan quickly in order to limit his total interest expense. Debt Definition@Investopedia
Interest is charged by lenders as compensation for the loss of the asset's use. In the case of lending money, the lender could have invested the funds instead of lending them out. With lending a large asset, the lender may have been able to generate income from the asset should they have decided to use it themselves.Interest Rate Definition @Investopedia
Common debt connects the present to the future. From the creditor's perspective, interest represents, among other things, the reward for deferring present consumption or other use (not to mention hiding the money under a mattress), including a reward for risk of default and some protection against expected inflation (etc.). That is to say, expectations about possible outcomes into the future enter into the rate of interest she will charge. (I return to this below.)
From the debtor's perspective debt allows one to shape the future. So, with a mortgage one can, say, turn a logically and physically possible house, into a real house. With a loan, an ecological entrepreneur can turn a dream of a wind-farm that generates clean energy into reality. That is to say, particular loans connect the present to possible worlds that are actualized in virtue of, at least in part, these loans.* It's possible, of course, that there are other means to the roughly same possible future without these loans (the house was build with a bequest not a mortgage, etc). So, I am not suggesting that the existence of this loan can help provide identity conditions or precisification of a possible world.
During a guest lecture on the Greek debt crisis by a high ranking civil servant of the Dutch Treasury, Michel Heijdra (a trained and rather gifted philosopher) remarked (something to the effect) that interest on debt also represent an optimistic view of the future. For, its rate tends to exceed risk-free income as well as other uses (present pleasure in consumption, etc.) that represent a status quo bias. This made realize that within the class of possible worlds from any given production possibility frontier that may be actualized in virtue of contracted debt (recall also this post on Piketty's idea of a technological frontier), interest-bearing debt actualizes a particular sub-set of these. In fact, the sub-set of these are biased toward the generation of income that can cover and repay the principal and interest on it. In a larger equilibrium framework, these are optimal, Leibnizian worlds. I mention Leibniz not just because the optimization techniques he (and his followers, Bernoulli, Euler, etc.) pioneered are still central to how economics thinks of such matters, but also because these remarks are very much in the spirit of his remarks on possible worlds and the role of God as optimizer and economizer in it (see, e.g., Rescher).**
Obviously, not all debt will be repaid. Interest on common debt also represents a reward of risk and this entails some probability of default. So, in practice debt, makes us aim for Leibnizian possible worlds while allowing for the genuine possibility that locally we land on sub-optimal worlds, including worlds that are worse than the present one in which the debt is not repaid and the borrower scrambles for other funds. (The preceding sentence is not an attack on Leibniz (who can easily accommodate the insight.)) So, we may say, then, that common debt connects us to possible worlds that our close to optimal*** given present endowments and possible worlds that are rather annoying from the present perspective. The former ought to predominate, but the latter cannot be ruled out.