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- Topic: EAR Question
| Author | Topic: 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% Answer: 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. |
