RATE( ) function

Returns the interest rate per period.

Syntax

RATE(periods, payment, amount)

Parameters

Name Type Description
periods numeric

The total number of payment periods.

payment numeric

The payment per period.

amount numeric

The principal amount of the loan.

Note

The RATE( ) function assumes that payments are made at the end of each period.

Output

Numeric. The rate is calculated to eight decimals places.

Examples

Basic examples

Returns 0.00541667 (0.54%), the monthly interest rate implied by a twenty-five year, $275,000 loan with monthly payments of $1,856.82:

RATE(12*25, 1856.82, 275000)

Returns 0.06500004 (6.5%), the annual interest rate implied by the same loan:

RATE(12*25, 1856.82, 275000)*12

Advanced examples

Converting the nominal rate to the effective rate

The RATE( ) function calculates the nominal interest rate. You can use the EFFECTIVE( ) function to convert the result of RATE( ) to the effective interest rate.

Returns 0.06715155 (6.7%), the effective annual interest rate implied by the loan in the examples above:

EFFECTIVE((RATE(12*25, 1856.82, 275000)*12), 12*25)

Annuity calculations

Annuity calculations involve four variables:

  • present value, or future value $21,243.39 and $ 26,973.46 in the examples below
  • payment amount per period $1,000.00 in the examples below
  • interest rate per period 1% per month in the examples below
  • number of periods 24 months in the examples below

If you know the value of three of the variables, you can use an Analytics function to calculate the fourth.

I want to find: Analytics function to use:
Present value

PVANNUITY( )

Returns 21243.39:

PVANNUITY(0.01, 24, 1000)
Future value

FVANNUITY( )

Returns 26973.46:

FVANNUITY(0.01, 24, 1000)
Payment amount per period

PMT( )

Returns 1000:

PMT(0.01, 24, 21243.39)
Interest rate per period

RATE( )

Returns 0.00999999 (1%):

RATE(24, 1000, 21243.39)
Number of periods

NPER( )

Returns 24.00:

NPER(0.01, 1000, 21243.39)

Annuity formulas

The formula for calculating the present value of an ordinary annuity (payment at the end of a period):

The formula for calculating the future value of an ordinary annuity (payment at the end of a period):

ACL Scripting Guide 14.1