# CPCU® 540 Formulas

The CPCU® 540 exam is very difficult and heavily math intensive. According to nationally published CPCU® pass rates, the CPCU® 540 is the hardest CPCU® exam. The pass rate is typically around 72%, primarily because there are over 80 formulas to memorize.

In this resource, we’re going to breakdown the most important formulas that you need to memorize to pass the CPCU® 540 exam. This comes straight from our CPCU® 540 online course where we provide a detailed breakdown of the most important formulas of each chapter, along with our difficulty and importance rank for each chapter.

## CPCU® 540 – Formulas You Don’t Need to Memorize

First, you should know what formulas you do NOT need to memorize. At your exam, you will be given a small list of select formulas to use on the CPCU® 540 exam. The list of formulas provided to you on the CPCU® 540 exam includes:

• Future Value Over a Single or Multiple Period
• Future Value Over Multiple Periods With Payment Periods Less Than One Year
• Present Value Over a Single or Multiple Periods
• Future Value of an Annuity
• Present Value of an Annuity
• Present Value of a Perpetuity
• Net Present Value

For the full list of formulas that are provided and those that are NOT provided at the CPCU® 540 exam, download our formulas list and practice exam.

## CPCU® 540 – Most Important Formulas (Must Memorize)

According to the nationally published estimates, there are 34 math formulas that you’ll be required to know to pass the CPCU® 540 exam.  Of these 34 formulas; 7 of them are provided to you at the exam and 27 are not provided to you at the exam (meaning you’ll have to memorize the formula). You can download those lists here, but unfortunately, this greatly underestimates the number of formulas that you’ll need to memorize for the CPCU® 540 exam. According to our count, there are approximately 80 CPCU® 540 formulas that you should know before taking the CPCU® 540 exam.

These are the 3 most important formulas on the CPCU® 540 exam:

• Present and future value tables
• CAPM
• Annual rate of return

#### Present and future value tables

As mentioned above, you will be given these formulas on the CPCU® 540 exam but you WON’T be given the formulas or instructions on how to calculate present value and future value using the tables. You will be given four tables to use on the CPCU® 540 exam:

• Future value table
• Present value table
• Future value annuity table
• Present value of annuity table

These tables provide an easier way of calculating the future value and present value. Each table provides a factor, use the tables to find the factor that corresponds with period (n) on the left-hand side of the table and interest rate (r) at the top of the table. You MUST know how to use these tables, it is vitally important to passing the CPCU® 540 exam. I argue that this is the most important aspect of the CPCU® 540 exam. Using the future value and present value tables are more accurate (because you’re not punching numbers in a calculator) and will save you lots of time.

If you do not have a copy of the future value and present value tables, you can download them here along with the formulas list and CPCU® 540 practice exam.

There are six primary present and future value formulas. Here are the present and future value table formulas, I’ve abbreviated future value to “FV” and present value to “PV”:

• Future Value  = PV × FV Factor
• Future Value Over Multiple Periods With Payment Periods Less Than One Year = PV × FV Factor (you must calculate period and interest based on the number of payments within a period)
• Present Value Over a Single or Multiple Periods = FV × PV factor
• Future Value of an Annuity = Annuity payment × FV Annuity Factor
• Present Value of an Annuity = Annuity payment × PV Annuity Factor
• Present Value of a Perpetuity = Annuity payment × PV Annuity Factor

In addition to these six primary present and future value formulas you must also know how to calculate:

• Present value annuity due
• Future value annuity due
• Present value of unequal payments
• Net present value

#### CAPM

Cost of equity (CAPM) = risk-free rate + Beta (expected market return – risk-free rate)

• Beta – the Beta is a measure of risk compared to the market as a whole.
• Market return – the expected market return is the expected return from the overall market. For stocks, this is usually represented by the S&P 500
• Risk-free rate – risk-free rate of return is the theoretical rate of return an investor could earn by investing in an investment vehicle with zero risk. This represents the market rate of interest an investor would expect from an absolutely risk-free investment, such as a treasury bill, which is risk-free because it is backed by the government and guaranteed to pay.

#### Annual rate of return

Two rate of return formulas you must know:

• Bond annual rate of return = (coupon + capital gain) ÷ bond price beginning of year
• Stock annual rate of return = (capital gain + dividends) ÷ stock price beginning of year

These two formulas are vitally important to the CPCU® 540 exam. These two questions come from chapter 8 of the CPCU® 540 course, one of the most important chapters of the CPCU® 540 exam. The annual rate of return formulas can be re-arranged to solve for coupon rate, beginning bond price, and beginning stock price. You’ll need to know this formula inside and out, make sure you know how to calculate the rate of return and how to re-arrange the formula.

## CPCU® 540 Formula Review

The formulas are the most important aspect of the CPCU® 540 exam. Ensure you memorize the most important formulas detailed above if you don’t memorize these key formulas it will be very very difficult to pass the CPCU® 540 exam. For a list of everything we’ve talked about in this blog including the formulas provide to you on the exam, the formulas not provided to you on the exam, present/future value tables, and a free practice exam, download our free CPCU® 540 bundle:

Disclaimer

Remember, every CPCU® exam is different. No single exam is the same. Be sure to study ALL topics (not just our recommendation). This resource is intended to provide you with a general idea of where your focus should be. Make sure to thoroughly study every topic of this exam.

Difficulty rank, importance rank, and the advice provided in this resource are solely the opinion of AssociatePI. This resource is intended to provide you with a general idea of where your focus should be. Each exam administered by The Institutes is different. AssociatePI is not affiliated with The Institutes or involved in the exam writing process. Please be sure to thoroughly study every chapter and every topic of this course.

CPCU® exams are administered by the American Institute for Chartered Property Casualty Underwriters (“The Institutes”). AssociatePI does not administer the actual exams, we are an independent resource of free content, advice, and study material for professional insurance education. This blog is intended for informational purposes only, to inform prospective students of the benefit of the CPCU® designation.

CPCU® and API are trademarks of the American Institute for Chartered Property Casualty Underwriters (“The Institutes”). AssociatePI LLC is not affiliated with, associated with, endorsed by or otherwise supported or recognized by The Institutes in any way. AssociatePI LLC is not authorized by The Institutes to offer courses, practice examinations, or any other resources related to the Institutes’ designations or other programs.

For further information, please email [email protected].

### FREE PRACTICE EXAM.  