# How to use the RRI function

**What is the RRI function?**

The RRI function calculates the growth of an investment in percent per period.

#### Table of Contents

## 1. Introduction

**What is the difference between the RRI function and the RATE function?**

RRI calculates the net rate of return for an investment based on the invested value and future value.

RATE calculates the periodic interest rate required to achieve a certain future value from given cash flows, invested value, and future value.

RATE(nper, pmt, pv, [fv], [type])

RRI(Nper, Pv, Fv)

**What is an investment?**

An investment is an asset or business acquired with the goal of generating income or appreciation, the purpose is to grow the money over time.

**What are periods?**

A payment period is the length of time between payments made on a loan or investment. For example, a loan with monthly payments the payment period would be one month. A loan with quarterly payments the payment period would be three months.

**What is present value?**

The present value is the initial amount that will earn interest/dividend.

**What is future value?**

The compounded amount after the calculated periods based on the given rate. It measures what a current capital (present value) amount will be worth at a designated future date.

**What are periodic constant payments?**

Periodic constant payments are payments that are made at regular intervals such as monthly, quarterly, or yearly and have the same amount each time.

**What is a constant interest rate?**

A fixed interest rate is an interest rate that remains the same throughout the term of a loan or an investment.

**What is the number of compounding periods per year?**

The number of compounding periods per year refers to how often interest is compounded annually on an investment or loan.

Some common compounding periods:

- Annually - 1 compounding period per year
- Semiannually - 2 compounding periods per year
- Quarterly - 4 compounding periods per year
- Monthly - 12 compounding periods per year
- Weekly - 52 compounding periods per year
- Daily - 365 compounding periods per year

**What is compounding?**

Compounding refers to the process of generating more interest from interest that was previously earned. It causes interest to grow exponentially over time.

**Related functions**

Function | Description |
---|---|

RATE(nper, pmt, pv, [fv], [type]) | Returns the interest rate per period of an annuity |

PV(rate, nper, pmt, [fv], [type]) | Returns the present value of an investment. |

FV(rate, nper, pmt, [pv], [type]) | Returns the future value of an investment. |

PDURATION(rate, pv, fv) | Returns the periods needed for an investment to reach a future value. |

**How is the RRI Function calculated?**

RRI = (Fv/Pv)^{(1/nper)}

Fv - future value

Pv - present value

nper - periods

The equivalent formula is:

## 2. Syntax

RRI(*Nper, Pv, Fv)*

Nper |
Required. Nper is the number of periods. |

Pv |
Required. Pv is the present value. |

Fv |
Required. Fv is the future value. |

## 3. Example 1

**You have invested $1,000 in a fixed deposit account that promises to grow to $2,000 over 24 years. What is the rate of return per period for this investment?**

The arguments are:

nper: 24 periods (years)

Pv: 1,000 (present value)

Fv: 2,000 (Future value)

The RRI function calculates the growth, in percent of a period, of an investment based on the future value.

Formula in cell C21:

The formula in cell C21 returns 2.93% which represents the growth per period for an investment of 1,000 to grow to a future value of 2,000 in 24 periods.

The math formula behind the RRI function is: RRI = (Fv/Pv)^{(1/nper)}

Lets plug the argument values in this math formula and see what we get.

(2000/1000)^{(1/24)}

becomes

2^{(1/24)} equals 1.0293022366 This value matches the calculated value in cell C21.

## 4. Example 2

**You want to save $50,000 for your child's college education in 12 years. If you start with an initial investment of $20,000, what rate of return per period do you need to achieve your goal?**

The arguments are:

nper: 12 periods (years)

Pv: 20,000 (present value)

Fv: 50,000 (Future value)

The RRI function calculates the growth, in percent of a period, of an investment based on the future value.

Formula in cell C21:

The formula in cell C21 returns 7.93% which represents the growth per period for an investment of 20,000 to grow to a future value of 50,000 in 12 periods.

The math formula behind the RRI function is: RRI = (Fv/Pv)^{(1/nper)}

Lets plug the argument values in this math formula and see what we get.

(50000/20000)^{(1/12)}

becomes

2.5^{(1/12)} equals 1.079348438 This value matches the calculated value in cell C21.

## 5. Example 3

**You have the opportunity to invest in a startup that requires an initial investment of $25,000. The startup promises to return 4 times the initial value after 8 years. What is the rate of return per period for this investment?**

The arguments are:

nper: 12 periods (years)

Pv: 20,000 (present value)

Fv: 100,000 (Future value)

The future value is 4 times larger than the initial investment. Formula in cell C19:

The RRI function calculates the growth, in percent of a period, of an investment based on the future value.

Formula in cell C21:

The formula in cell C21 returns 18.92% which represents the growth per period for an investment of 25,000 to grow to a future value of 100,000 in 8 periods.

The math formula behind the RRI function is: RRI = (Fv/Pv)^{(1/nper)}

Lets plug the argument values in this math formula and see what we get.

(100000/25000)^{(1/8)}

becomes

4^{(1/8)} equals 1.01892 This value matches the calculated value in cell C21.

The table below the formula in cell C21 calculates the growth for each period starting with period 0 (zero) that has the initial investment. The formulas in cells B27, C27, and D27 are dynamic meaning they change automatically when the input values in cells C18, C18, and C19 changes.

Excel dynamic array formula in cell B27:

The formula in cell B27 calculates the number of periods based on input value in cell C17. It always starts with 0 (zero).

Excel dynamic array formula in cell C27:

The formula in cell C27 calculates how the initial investment grows, it shows the growth for each period.

Excel dynamic array formula in cell D27:

This formula repeats the percentage growth for each period.

## 6. Why is this function not working

The RRI function returns:

- #VALUE! error if arguments
*are*not a valid data type. - #NUM! error if the arguments are not valid.

### Functions in 'Financial' category

The RRI function function is one of 27 functions in the 'Financial' category.

### Excel function categories

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### 2 Responses to “How to use the RRI function”

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I think the equivalent formula is =(C4/C3)^(1/C2)-1. Otherwise, you get 102.93%.

Thank you Greg. You are right.