## Purpose

## Return value

## Syntax

`=RATE(nper,pmt,pv,[fv],[type],[guess])`

*nper*- The total number of payment periods.*pmt*- The payment made each period.*pv*- The present value, or total value of all loan payments now.*fv*- [optional] The future value, or desired cash balance after last payment. Default is 0.*type*- [optional] When payments are due. 0 = end of period. 1 = beginning of period. Default is 0.*guess*- [optional] Your guess on the rate. Default is 10%.

## How to use

The RATE function returns the interest rate per period of an annuity. You can use RATE to calculate the periodic interest rate, then multiply as required to derive the annual interest rate. The RATE function calculates by iteration. If the results of RATE do not converge within 20 iterations, RATE returns the #NUM! error value.

The RATE function takes six separate arguments, three of which are required as explained below.

*nper* (required) - The total number of payment periods in the annuity. For example, a 5-year car loan with monthly payments has 60 periods. You can enter *nper* as 5*12 to show how the number was determined.

*pmt* (required) - The payment made each period. This number cannot change over the life of the annuity. In annuity functions, cash paid out is represented by a negative number. Note: If *pmt* is not provided, the optional *fv* argument must be supplied.

*pv* (optional) - The present value. This is the cash balance required after all payments have been made.

fv (optional) - The future value, or a cash balance required after the last payment is made. When *fv* is omitted, it defaults to zero (0) and *pmt* must be provided.

*type* (optional) - *type* is a boolean that controls when when payments are due. Use 0 for payments due at the end of the period (regular annuities) and 1 for payments due at the end of the period (annuities due). *Type* defaults to 0 (end of period).

*guess* (optional) - *guess* is a seed value to use for iteration. When omitted, *guess* defaults to 10%. Ordinarily, you can safely omit *guess*. If RATE does not converge, RATE will return a #NUM! error. Try different values for *guess *between 0 and 1.

### Example

To calculate the annual interest rate for a $5000 loan with payments of $93.22 per month over 5 years, you can use RATE in a formula like this:

```
=RATE(60,-93.22,5000)*12 // returns 4.5%
```

In the example shown, the formula in C10 is:

```
=RATE(C7,-C6,C5)*C8 // returns 4.5%
```

Notice the value for *pmt* from C6 is entered as a negative value.

### Notes

You must use consistent values for for *guess *and* nper.* If you make monthly payments on a five-year loan at 10 percent annual interest, use 10%/12 for *guess *and 5*12 for* nper*. If you make annual payments on the same loan, use 10% for *guess* and 5 for *nper.*