<p>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.</p>

<p>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.</p>

<p>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.</p>

<p>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€.</p>

CC BY-SA 4.0
2019-06-24T14:57:48.777Z
@Giskard, very good point thank you. I've edited the answer.
BB King
CC BY-SA 4.0
2019-06-24T23:54:35.190Z
@Giskard where did your comment go? ;)
Frank Swanton
CC BY-SA 4.0
2019-06-24T09:03:42.980Z
2019-06-24T14:57:28.387Z
2019-06-24T14:57:28.387Z
BB King
<p>I am reading a macro-finance article that deals with asset financing.</p>

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

<p><span class="math-container">$\textbf{My Question}:$</span> How do you interpret the difference between <span class="math-container">$R$</span> and <span class="math-container">$r$</span>? Is it conventional to define net interest in macro-finance literature in this way?</p>

<macroeconomics><interest-rate>
Gross interest rate ($R$) v. Net interest rate ($R-1$)
Frank Swanton
# Gross interest rate ($R$) v. Net interest rate ($R-1$)

(Asked by: username_0 on 2019-06-24)

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?

**Tags:** macroeconomics, interest-rate


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## 1 answers

### Answer by username_1 on 2019-06-24. Score: 2 | Accepted answer

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€.

> **Comments:**
> **username_1**: @Giskard, very good point thank you. I've edited the answer.  
> **username_0**: @Giskard where did your comment go? ;)  

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