You are quoted a yearly rate 8.25% compounded semi-annually. What is the effective quarterly rate? A. 8.25% B. 2.0625% C. 4.1675% D. 2.0417%
| Annual rate of interest compounding semi annually | 8.25% | ||||||||
| Effective annual interestt rate (1+0.04125)^2 -1 | 8.42% | ||||||||
| Now, Compounding Quarterly means compounding done 4 times yield same annual effective interest rate | |||||||||
| Therefore | |||||||||
| Effective rate = 8.42% | |||||||||
| Quarterly rate= ? | |||||||||
| Period = 4 | |||||||||
| Formula | |||||||||
| Effective rate = (1+ Rate)^ period - 1 | |||||||||
| 0.0842 = (1+ rate)^ 4 - 1 | |||||||||
| Therefore r= 0.020417 | |||||||||
| Quarterlty rate = 2.0417% | |||||||||
| Answer is D. 2.0417% | |||||||||
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