CFA CFA Level 1 Diffenece between various rates of interest

# Diffenece between various rates of interest

• Author
Posts
• 0

i know what an effective intt rate is. and also stated rate concept is clear.
but how do u know which is which in a question. it always seem the opposite to me.
also BEY, is that just the double of semi annual effective?
Can someone pls clear this confusion?

• 4

For instance:
“A bank promises that with its monthly compounding plan, a \$10,000 deposit today will grow into \$15,000 in 4.5 years. What must be the annual percentage rate (APR) and the effective annual rate (EAR) on this account?
(a) APR= 9.43% EAR= 9.04%
(b) APR= 9.43% EAR= 9.84%
(c) APR= 9.04% EAR= 9.43%”
what i thought was n=54, pv=10000 fv=15000, so i=.75. hence, ear= 9.04
and i reasoned that this has to be ear because ear is that rate of intt u earn effectively including the compounding,
so i went with a.

so, if not that, what is bey?

• 3

can you give an example of questions where you were not sure which one they were mentioning? because it’s kind of hard to explain how they ask it, usually its the regular yearly rate –> so you transform it into effective or whatnot

BEY is technically speaking a “double” of semi annual hhaha you may think of it that way I suppose, as long as you know how to convert between rates

@aanchalb

• 3

@vincentt could u explain by what logic did u deduce that the 9.429% u calculated is ear? (because by taking n as 4.5, u did not take the effect of compounding, so how is it ear?)
what is wrong with my reasoning?

• 3

so according to me,
Stated rate of interest, a.k.a APR is the annual rate of simple interest.
EAR is the effective rate of interest which is just stated rate but compounded interest.
therefore, EAR will be greater than APR, as it accounts for interest on interest.

Am i even remotely close to the real concept?
My whole understanding on this tiny topic is the reason all my numerical questions are incorrect.

• 3

@vincentt yes this helps.
Thank u so much.

• vincentt
Participant
• CFA Level 3
2

likewise, you could also use N=54 and you would get the rate of 0.75xx when you CPT I/Y.

from there
* 12 would be the simple rate (APR)
or
^ 12 would be the compounded rate (EAR)

• 1

I agree with how vincentt did this

the yield that your financial calculator gives you would be the effective rate to transform the initial 10,000 deposit into 15,000 -> EAR

• vincentt
Participant
• CFA Level 3
1

@aanchalb yup that’s right APR is simple and EAR is compounded.

So by using what you did N = 54; PV = -10,000; FV = 15,000; CPT I/Y = 0.75369% (the rate for 1 month)

Then to annualised it, here are the steps:

APR (simple or non compounding)

0.75369% * 12 = 9.04428%

EAR (compounding)

0.75369% —to compound you have to convert to decimals—> 0.0075369

To annualise it 1 + rate to the power of 12:

( 1 + rate) ^ 12 = ( 1 + 0.0075369) ^ 12 = 1.094288 – 1 = 0.094288 –> 9.4288%

Hope that helps.

• vincentt
Participant
• CFA Level 3
0

N=4.5 PV=-10,000 FV = 15,000
CPT I/Y = 9.429%

That would be EAR i supposed.

Then get the monthly rate (since it’s compounded –> (1 + r )^(1/12) )
so (1 + 0.09429 ) ^ 0.08333 = 1.007537 = 0.7537% (monthly rate)

Since APR is a simple rate (not compounded) 0.7537% * 12 = 9.04%

BEY = bond equivalent yield which i don’t think is relevant in your context –> (6-month rate) * 2