# What does discrete return mean?

## What does discrete return mean?

Discrete numbers and investments have a distinct set of possible values rather than a continuous set. In other words, the number can only be an integer or some predefined value. Calculating a discrete return makes the number much more concrete. A common discrete return is a compound interest rate.

Why is there a difference between discrete annual and continuous compounding?

Under periodic or discrete compounding, accrued interest is added to your account after a fixed amount of time, such as each day, month or year. With continuous compounding, interest is earned on your account continuously, and instantly accrues more interest on the interest.

What is continuous return?

Continuously compounded return is what happens when the interest earned on an investment is calculated and reinvested back into the account for an infinite number of periods. Regular compounding is calculated over specific time intervals such as monthly, quarterly, semi-annually and on an annual basis.

### What is the difference between compound interest and continuous interest?

The real interest rate you get after one year including compound interest is called the effective (yearly) interest rate. Continuous compound interest is when you make the compounding time interval infinitely small.

How are discrete returns different from discrete returns?

In the end of every period interest is paid and reinvested. First we see that discrete returns are not additive: But discrete returns are multiplicative. This can be proofed again using induction: For continuous returns interest is paid continuously and not only at discrete points in time. We have:

What’s the difference between discrete and continuous compounding interest?

Compounding interest calculates interest on the principal and accrued interest. When interest is compounded discretely, its formula is: Continuous compounding introduces the concept of the natural logarithm. This is the constant rate of growth for all naturally growing processes. It’s a figure that developed out of physics.

## How is interest paid in a continuous return?

For continuous returns interest is paid continuously and not only at discrete points in time. We have: You can proof that continuous returns are additive using induction for a last time: Want to learn more about optimizing investment strategies and improving analytics?

What’s the difference between discrete and continuous data?

For example, you can measure your height at very precise scales — meters, centimeters, millimeters and etc. You can record continuous data at so many different measurements – width, temperature, time, and etc. This is where the key difference with discrete data lies. The continuous variables can take any value between two numbers.