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
“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.
correct answer was c.
so, if not that, what is bey?
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
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.
@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%
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.
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