AuthorTopic: EAR Question
Uruz713
@2014-12-01 18:48:53
I don't know if I've just been studying too long, but this question is tripping me up despite how basic it is.

"If an investment of \$4,000 will grow to \$6,520 in 4 years with monthly compounding, the effective annual interest rate will be closest to:
A) 11.2%
B) 12.3%
C) 13.0%

C) 13.0%

Can someone explain why the number of compounding periods for this question is 4 and not 4*12=48, which would've yielded answer B) 12.3% ?
turtle30
@2014-12-02 11:14:35
question asks effective annual rate n=4
cfa1310
@2014-12-12 15:51:29
are you sure that's the right question? Its 13% when you have the annual interest rate not effective annual interest rate
SeanDec10
@2014-12-22 20:03:02
effective annual rate is computed on an annual basis. Doesn't matter how often it is actually compounded.
SeanDec10
@2014-12-22 20:10:22
Here is a more complete answer:

Total return = 63%
Periodic Return = 1.62^(1/48) - 1 = 1.0231%
EAR:
(1.01231)^12 - 1 = 13.0%

When you annualized the periodic return, you are effectively doing (1.62^(12/48) which is 1.62^(1/4)
Mikehuynh
@2014-12-22 20:50:37
PV = -4000
FV = 6520
N = 48
=> I/Y = 1.0231*12 = 12.2769 => annual percentage rate

=> you have to convert to EAR = 12.9918

So C is the correct answer. Hope can help Uruz713
anova
@2017-02-21 15:35:22
fv=pv(1+r)^n
6520=4000(1+r)^48
r=(6520/4000)^(1/48)-1
r=0.010231
Annual rate= (0.010231*12)*100%= 12.2769%
Effective Annual Rate=[(1+12.2769/12)^12-1]*100%
EAR=12.9918% which corresponds to option C.
This can be done in fewer steps once you get the hang of it.