Calculating the Rate, i

Note that due to the placement of i in the PV & FV formulas for ordinary annuities, it is not possible to solve for i algebraically.  Excel has a function we can use to solve for i.

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

where:

  • Nper  is the total number of payment periods in an annuity.
  • Pmt  is the payment made each period
    • If pmt is omitted, you must include the fv argument.
  • Pv is the present value
  • Fv is the future value,
    • If fv is omitted, it is assumed to be 0 and you must include the pmt argument.
  • Type is the number 0 or 1 and indicates when payments are due.
    • 0 indicates at the end of the period
    • 1 indicates at the beginning of the period
    • If type is omitted, it is assumed to be 0

Example 1

A life insurance company advertises that $50,000 will purchase a 20-year annuity paying $341.13 at the end of each month. What nominal rate of return and effective rate of return does the annuity investment earn? (Source: Jerome & Worswick, 2020, Example 12.3A).

For this example we are given:

  • Compounding/payment frequency = 12
  • PMT = $341.13
  • PV = $50,000
  • FV = 0
  • Type = 0
  • Number of years: 20

We can set up our spreadsheet to calculate the nominal and effective rates.

screenshot of Excel spreadsheet for calculating RATE

Try recreating the spreadsheet above on your own. 

Click this link to see the completed spreadsheet: Calculating periodic, nominal and effective rates in an annuity – Template

For more information about using the RATE function, see Microsoft Support

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Using Excel in Business Math Copyright © by Lisa Koster is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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