# Rate of Return Calculator

By Tibor Pal, PhD candidate
Last updated: Sep 03, 2021

The rate of return calculator allows you to find the annual rate of return of a given investment, which is the net gain or loss through a given period expressed as a percentage of the initial investment cost.

Note, that the present tool allows you to find the annual rate of return on an investment, with the option to provide regular cash flows during the investment period. If you would like to find the internal rate of return (IRR) of an investment with irregular cash flows, use our IRR calculator.

In the following, we explain what the rate of return is, how to calculate the rate of return on investment, and you can get familiar with the rate of return formula.

## What is rate of return?

As you probably know, the fundamental principle of investing money is to receive more money in the future than you provided at the beginning. In other words, investors expect a positive rate of return on their investment. In finance, we call it a required rate of return because the opportunity for more money in the future is required to convince investors to give up money today.

However, keep in mind that the rate of return may have different meanings depending on its context. For example, if it is positive, it suggests profit from an investor's viewpoint, but from the investee's perspective it represents a cost. For debt, we call this cost the interest rate. For equity, we call it the cost of equity, consisting of dividends and capital gains. Therefore, the rate of return can indicate either the cost of money or the price of money.

## The rate of return definition

In finance, a return is a profit on an investment measured either in absolute terms or as a percentage of the amount invested. Since the size and the length of investments can differ drastically, it is useful to measure it in a percentage form and to compute for a standard length when comparing. When the time length is a year, which is the typical case, it refers to the annual rate of return or annualized return. If the investment performance is measured as return per dollar invested, we call it the return on investment (ROI).

There are other measures which reflect return from different perspectives:

## How to calculate rate of return on investment - the rate of return formula

We can compute the rate of return in its simple form with only a bit of effort. In this case, you don't need to consider the length of time, but the cost of investment or initial value and the received final amount.

`rate of return = (final amount received - initial value) / initial value`

If the rate takes a negative form, we have a negative return, representing a loss on the investment, assuming the amount invested is greater than zero.

When we would like to account for the time length and effect of reinvested return, in particular the compounding frequency, things become tricky.

The fact is, at least according to mathematicians, there is no straightforward formula that can give an exact solution to find the rate of return. A traditional technique for such a problem is to employ the iteration method, which is a series of approximations leading us to the right answer. In our case, the iteration is made with the following rate of return formula (`ROR`):

`FV = PV * (1 + ROR)ⁿ + Pmt * (1 + ROR)ⁿ⁻¹`

where:

• `FV` - Final amount received;
• `PV` - Initial investment; and
• `Pmt` - Periodic cash flow.

Since this procedure would take a considerable time and effort, we use one of the most common iterative technique in the present calculator, called the Newton Method, to find `ROR` from the rate of return equation above.

## How to apply the rate of return calculator?

The best way to get familiar with this tool is to consider three real-life examples. To simplify things, all the following examples involve yearly compounding and annual cash flows (if applicable).

1. Finding the rate of return with positive cash flows

Example 1

Steve got 1,000 dollars as a gift ten years ago and he gave it to his older brother, a professional investor. During these 10 years, Steve gave his brother 100 dollars at end of each year, and now his brother has return 5,000 dollars to him. What rate of return Steve earned?

The precise answer is `12.379%`, which appears if you set the initial investment to `\$1,000` with a final amount of `\$5,000`, `10` years investment length, and `\$100` periodic deposit.

1. Estimating the rate of return with interim cash flows

Example 2

You just acquired an annuity, a financial product usually provided by insurance companies, that will pay you 5,000 dollars annually for ten years, and you receive the first payment today. Your friend, Jack, offers you 40,000 dollars for the annuity. If you sell it to him, what rate of return will Jack earn on the investment?

How to find rate of return in this case? Your friend's initial investment is `\$40,000` dollars with a zero final amount received but `5,000` dollars withdrawals for `10` years. Keep in mind that you need to write `-\$5,000` as withdrawals to represent a negative cash flow.

After setting these variables, you will immediately know that Jack will gain a `4.277%` return annually with the total withdrawal of `\$50,000`.

Example 3

You just became a beneficiary of a life insurance policy. The insurance company gives you a choice of 100,000 dollars today or a 10-year annuity of 12,000 dollars at the end of each year. What rate of return is the insurance company offering? How do you calculate rate of return with our calculator?

In this case, when you set `\$100,000` as an initial investment and `-\$12,000` for the periodic withdrawals, you will see that rate of return is `3.46%` with a total withdrawal of `\$120,000`.

Note, that in the present calculator, we deal with the nominal rate of return. If you would like to compute and learn about the inflation-adjusted real rate of return, please check our real rate of return calculator.

## Disclaimer

You should consider the annual rate of return calculator as a model for financial approximation. All payment figures, balances, and interest figures are estimates based on the data you provided in the specifications that are, despite our best effort, not exhaustive.

For this reason, we created the calculator for instructional purposes only. Still, if you experience a relevant drawback or encounter any inaccuracy, we are always pleased to receive useful feedback and advice.

Tibor Pal, PhD candidate
Main specifications
Initial investment
\$
\$
Investment length
yrs
Compounding method
Monthly
Interim periodic cash flows
Deposit or withdrawal
\$
Cash flow frequency
Monthly
Timing of periodic payment
End of period
Results
The rate of return is 16.203%.
Display
Chart of balances
People also viewed…

### Circumference

Use this free circumference calculator to find the area, circumference and diameter of a circle.

### Opportunity cost

The opportunity cost calculator helps you find out what that money you want to spend right now will be worth in the future. 