 # EAR - doing my head in...

these kinda question make me crazy … is there any clear cut rule to this folks? this questions at: http://www.analystforum.com/phorums/read.php?11,717397 http://www.analystforum.com/phorums/read.php?11,721571 like in the second case… why not multiply just 1.0231% by 12 ? why should it be compounded? thanks guys.

The second question is somewhat of a trick question. You have to know what information matters and what doesn’t. “If an investment of \$4000 will grow to \$6520 in four years with monthly compounding, the effective annual interest rate will be closest to?” So we know it’s a TVM calculation and we have the PV, FV, PMT, the things at question are N and I/Y. The question states that required is the effective ANNUAL rate, that tells you that you need to use years as that’s all the relevant info you have. Plug in: PV= -4000, PMT = 0, FV = 6520, Computer I/Y

The second question is definitely trickier. The question is asking what’s the eay rate. PV and FV is given. So 4000 is growing to 6520 in 4 years. That’s all you know, whether the money is growing daily or monthly or some other time frame you dont care, because you know it took it all in all 4 years to go from 4k to 6520. So simply plug in the information given and you’ll get the answer. Another way to do this problem is and to think about it is in geometric mean, your return = 2520 / 4000 for four years. so you grow your money 63% in 4 yrs. so effectively how much did you grow your money in 1 year? 1.63 ^.25 - 1 = 12.99

Below you will find some explanation of what the EAR really is, but for this problem the answer is very easy and does not require a calculator at all. You know that \$4000 becoming \$6520 in 4 years has an annual compunded return of, or EAR: EAR = [(\$6520/\$4000)^0.25] -1 = 0.1299, where 0.25 is 1/years = 1/4years=0.25. That’s it for this problem. 1) For any return, there is something called a stated rate, which is an annual rate, like when you go to the bank and the bank says we’ll take your deposit for 5.25%. Here they the annual stated rate. Or if you grow a certain sum over 5 years, compounded daily or whatever, you still will talk about the stated annual rate, or the annual percentage rate (APR). 2. That’s not the interesting rate, because what matters to you is the *actual* rate that you will actually get. That’s the effective annual rate. 3. So, how do I know what that effective annual rate (EAR) is? Simple: =======> 1. Ask how often do they compound your money? Monthly? quarterly? Daily? Or even continuously (every moment in time)? =======> 2. Lets say they told you that you’re a lucky guy because they compound it monthly. Then you take the stated rate (5.25%) and divide it by 12, add it to it 1, and raise it to 12 (to compund it 12 times): (1+APR/12)^12 = (1+0.0525/12)^12= 1.0538. Subtract 1, and you get an EAR = 5.38%, actually greater than what they *stated*. 4. The problem you asked for should have asked for the stated rate, because the EAR is straighforward.

It does matter whether it is monthly compounded or not. Let’s say it was quarterly compounded. N=16, PV=-4000, FV=6250, PMT=0…CPT I/Y= 2.8286 EAY=(1+0.028286)^4 - 1= 11.8%…So you do not get 12.99% anymore. I guess you got the correct answer by using N=4, PV=-4000, FV=6250 just because the calculator assumes monthly compunding.

calculator doesn’t assume anything all calculator knows is that its been given PV, and FV and Periods. it finds you the relevant interest for that period. simple.

Compounding in this case does not matter.

> N=16, PV=-4000, FV=6250, PMT=0…CPT I/Y= 2.8286 Check again.

compounding matters in this case, and compounding is the only assumption calculators work under. But the question is not asking you find the FV or PV, where it’d differ based on how you compounded. Question is asking you to output the yearly compounded rate of return. so when you put n = 4, you are telling calculator, there are 4 periods. give me the effective rate for each period. so calc will only give you the right answer, because it adjusts and sees which rate will work. let’s say calc returned 11 for instance, calc will immediately realize at 11 yearly rate you are not going to be able to make your 4k grow to 6520 so it gives you the rate at which it’ll grow to. whether the terms of the lending are not daily compounding or monthly or semianually, as long as its not greater than 1 year. the 1 yr rate return by the calc will always be the same.

I have entered 6250 instead of 6520…Sorry Yes, you are right…The result is the same…