Rate function

This article describes the formula syntax and usage of the RATE function in Microsoft Excel.

Description

Returns the interest rate per period of an annuity. RATE is calculated by iteration and can have zero or more solutions. If the successive results of RATE do not converge to within 0.0000001 after 20 iterations, RATE returns the #NUM! error value.

Syntax

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

Note: For a complete description of the arguments nper, pmt, pv, fv, and type, see PV.

The RATE function syntax has the following arguments:

• Nper    Required. The total number of payment periods in an annuity.

• Pmt    Required. The payment made each period and cannot change over the life of the annuity. Typically, pmt includes principal and interest but no other fees or taxes. If pmt is omitted, you must include the fv argument.

• Pv    Required. The present value — the total amount that a series of future payments is worth now.

• Fv    Optional. The future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is 0). If fv is omitted, you must include the pmt argument.

• Type    Optional. The number 0 or 1 and indicates when payments are due.

Set type equal to	If payments are due
0 or omitted	At the end of the period
1	At the beginning of the period

• Guess    Optional. Your guess for what the rate will be.

  • If you omit guess, it is assumed to be 10 percent.

  • If RATE does not converge, try different values for guess. RATE usually converges if guess is between 0 and 1.

Remarks

Make sure that you are consistent about the units you use for specifying guess and nper. If you make monthly payments on a four-year loan at 12 percent annual interest, use 12%/12 for guess and 4*12 for nper. If you make annual payments on the same loan, use 12% for guess and 4 for nper.

Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Data	Description
4	Years of the loan
-200	Monthly payment
8000	Amount of the loan
Formula	Description	Result
=RATE(A2*12, A3, A4)	Monthly rate of the loan with the terms entered as arguments in A2:A4.	1%
=RATE(A2*12, A3, A4)*12	Annual rate of the loan with the same terms.	9.24%