I am reading a macro-finance article that deals with asset financing.

While it defines the gross interest rate to be $R$, it defines the net interest rate to be $r\equiv R-1$. In equilibrium, the interest rate on one-period loan is said to be $R=\frac{1}{\beta}$, where $\beta$ is the discount factor applied to the dividends firms obtain over an infinite horizon.

$\textbf{My Question}:$ How do you interpret the difference between $R$ and $r$? Is it conventional to define net interest in macro-finance literature in this way?


It is often conventional. R is the amount of the loan plus the interest and r is just the interest rate. So R=1+r.

Suppose you borrow 100€ at a 10% interest rate. The interest you pay is 10€, since 10% of 100 is 10. That is where r comes in, with an interest rate of r=10%=0.1.

On the other hand, R is the rate implied by that interest rate r plus the original amount, so it is relevant for the total you pay back. Before adding interest payments, you must pay back 100% of the original loan or 1x the original loan, so R=1+r=110%=1.1.

So, in our example, with R you pay back 100×1.1= 110€, while with r we have a payment of 100×0.1=10€.

| improve this answer | |
  • 1
    $\begingroup$ @Giskard, very good point thank you. I've edited the answer. $\endgroup$ – BB King Jun 24 '19 at 14:57
  • $\begingroup$ @Giskard where did your comment go? ;) $\endgroup$ – Frank Swanton Jun 24 '19 at 23:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.