One of the most common mistakes made in when calculating DCFs and seen all too often in corporate finance analyses is forgetting to properly adjust an annual percentage rate for the period in question.

For example, if your cost of capital is 12% on an annual basis, and you’re valuing a project that lasts only a quarter, then the discount rate you use in your DCF analysis shouldn’t be 12% (the most common mistake), or even 3% (e.g. 12% / 4 quarters), but 2.87%.

Likewise, if you have a loan with an annual percentage rate of 6% and want to calculate the amount you’re paying each month, your effective rate each month isn’t 0.5% but 0.486%. Effective rates take the impact of compounding into account, whereas simply dividing one rate by the number of periods ignores this factor.

The formula for changing from an annual percentage rate to a semiannual, quarterly, or monthly one is straightforward. In general, given an annual rate:

Effective rate for period = (1 + annual rate)

Effective rate for period = (1 + annual rate)

^{(1 / # of periods)}– 1
So for monthly, quarterly, and semiannual rates, the math becomes:

**Monthly rate = (1 + annual rate)**

^{(1/12)}– 1**Quarterly rate = (1 + annual rate )**

^{(1/4)}– 1**Semiannual rate = (1 + annual rate)**

^{(1/2)}– 1Now that you understand the idea, use an online calculator to convert annual percentage rates to effective rates!

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## How to calculate net present value (NPV) - an introduction | Experiments in Finance

[…] I chose 5% as my discount rate in this valuation. I decided on this figure because I consider the amounts involved in running this site small and not very risky and more akin to putting the money in a savings account rather than anything else. After all, if the project fails, I quit running the site, and that’s that. The ads I run are done through pretty established companies that will pay when they’re supposed to. And I can’t very well invest the small amount I’m putting in each month nor the amounts I’m getting back in other places (like the stock market), so my opportunity cost is also minimal. Note that 5% is the annual rate, and I must change this to the appropriate periodic rate in order to calculate the NPV correctly. Using my periodic rate calculator, the monthly equivalent of 5% is around 0.407% or so. […]

## John Cutsinger

Thanks for the information. Now I need to take a performance return thats more than a year and convert it into an annualized number. I’m sure I just need to poke around a little.

## Glenn Sieja

I understand the conversion of the annual rate to a periodic effective rate.

In Excel, the directions for using the FV (Future Value) function indicate that we should take the annual rate and divide it by the period to get a periodic rate. Shoud we use the method described here instead?

Thanks

## Ricemutt

Hi Glenn,

I hate to punt on the question, but the answer is that it depends. If you’re given an APR (annual percentage rate), then you do as Excel says and divide by the period. If you’re given an APY (annual percentage yield), you’d need to take the compounding into consideration and use the periodic effective rate. (If you’re curious, I wrote an article last week on the differences between the two here).

At my last job, the corporation had a mandated discount rate of 15% per year to be used in all NPV analyses and we were instructed to use the effective periodic rate. This makes sense because in order to arrive at 15% annually, you’d have to take compounding into effect. If you didn’t, the annual discount rate would always be greater than 15%.

Hope that helps more than it confuses!

-Ricemutt

## nancy

how to convert an 8% cumulative return to a compounded return for a 3 year holding period.

## Ty

Can you provide the mathematical proof for converting an annual rate to a periodic (quarterly, monthly, etc.) rate. Thanks

## joyel rebello

i want to find out IRR of :-

Investment £100

monthly returns £10 per/month

period of 12 months or 1 year

will you please sent me the IRR of above question on my Email.

Thank you,

## William Lawrence

To convert a monthly IRR into an annualized IRR number, you use the following formula:

Annualized IRR = ((1+montly IRR)^12)-1

Do you agree?

Thanks

Bill

## Beck

Can I have an analysis of how you came to the formula?

Thanks

Beck

## Margie

Can somebody help me please, I need to calculate the effective interest rate, using compounding base on the formula below? Here are the given data:

Face value: $100,000

Period of payment: 5 yrs (annually)

Nominal rate: 12%

Net Price: $89,944

Effective interest rate: ?

Formula:

100,000(P/F,i,5)+100,000*12%(PA,i,5)

Thank you.

## lois

I am trying to learn how to calculate monthly amt to be received on a 2.36 interest rate on a figure of 100,000.00

## josh

THIS FORMULA IS INCORRECT. DO NOT TRUST IT

## baloo

WILLIAM LAWRENCE said :

To convert a monthly IRR into an annualized IRR number, you use the following formula:

Annualized IRR = ((1+montly IRR)^12)-1

Agree

But wat to do with the fornightly or weekly payments ????????

do tell me guys

## jatpapa

Can somebody please answer the question below.

ASSUMING THAT I MAKE MONTHLY PAYMENTS OF $30,000. AND HAS AN OUTSTANDING BALANCE AFTER 6 YEARS(OSB/72) OF $3,361,291,39. IF THE MARKET RATE FOR SIMILAR MORTGAGE IS j/2=12.25% and i make a down payment of $3,200.000. What would be the market value of the offer?

## john

Do you know the formula to convert a Ann/360 yield to a Semi 30/360 bond yield?

## Patrick

For NPV calculation, how do you calculate the discount rate table for 8% over a 5 year period ?

## Thom

If I am paying interest of 4% quarterly than how do I determine the rate this is on an annualized basis?? Can someone tell me the formula?

## kashifabbasrizvi

formula:

A=P(1+C)n

## Quan

to thom: your annual rate is calculated by this formula:

R(annual) = [(1+r(quarter rate))^4]-1

## YAhya

If my city has 3% of annual population growth rate what is the daily increase rate in growth and what is the monthly growth rate of the population. I f someone tell me the formula to calculate

## Deepak

Hi there, thanks for sharing some of the examples, i think you may be able to help me in my current anomaly.

Is it possible to get a single rate (something like an IRR) for a loan with floaring rates across periods, lets say on term of 5 years, 1st year 5%, second year 6% and third year 7% and 4th and 5th 8%, how can we calculate a single rate of interest of the entire term of the loan.

Please advise.

thanks

## Shane

hello can someone please help with this equasion.

A property is rented with rent collected at the end of each year. the rent for the coming year will be $23,500 to be collected in twelve mont’s time. The rent is expected to escaluate at 3% per annum.. THe property is expected to be worth $ 533043 at the end of 5 years.

What is the properties estimate of value using a discount of 13%.

With the value of the property to the nearest whole dollar.

any help appreciated . Can you use a DCF MOdel to figure this out etc.

## Royal

I appreciate you sharing this blog post.Really looking

forward to read more. Great.

## Pat

Read your equation, and wanted to find out why it worked. Took me awhile, but I was able to prove your equation using (P(1+i[1])^12n) = (P(1+i)^n) (which is pretty much the future worth of monthly compounding vs yearly compounding being equal to each other) and solving for i[1] as the monthly interest rate. Thanks a bunch for this!

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you arranged to borrow 3000 for home repairs. the loan will be required in 6 equal annual paymnets, with end of year payments at intest rate= 6% ( effective annual rate)

A. calculate the amount of yearly payment ( round to nearst doller)

B. after you have committ3ed to the loan payment in (a), the finance comppany informs you that there are some additional fees (transaction coast) abd these will be subtracted from the 3000 you are to recive. calculate the true intrst rate given these fees to be 180.

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What is the formula to add 350 basis points (annual) to a monthly return?

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The conversion of yearly rate to say monthly does not work. The formula you give does not yield the results of the calculator, nor those of the the example.

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