Asked by Natasha Finkelstein on May 13, 2024
Verified
Determine the equivalent nominal rate of interest compounded semi-annually, as 4.2% compounded monthly.
A) 4.20%
B) 4.24%
C) 4.28%
D) 4.36%
E) 4.44%
Nominal Rate
The rate of interest before adjustments for inflation or other factors that affect the true cost of borrowing or the real yield on an investment.
- Understand the process of converting between different compounding intervals.
Verified Answer
KH
Kyle- HananMay 17, 2024
Final Answer :
B
Explanation :
The equivalent nominal rate of interest compounded semi-annually can be found by first converting the monthly compounded rate to an effective annual rate (EAR) and then converting that EAR to a semi-annual nominal rate. The formula for converting a monthly compounded rate to an EAR is EAR=(1+rm)m−1EAR = (1 + \frac{r}{m})^m - 1EAR=(1+mr)m−1 , where rrr is the annual nominal rate (4.2% or 0.042) and mmm is the number of compounding periods per year (12 for monthly). Thus, EAR=(1+0.04212)12−1EAR = (1 + \frac{0.042}{12})^{12} - 1EAR=(1+120.042)12−1 . After calculating the EAR, convert it to a semi-annual nominal rate by using the formula for nominal interest rate, which is nominal rate=EAR×mnominal\ rate = EAR \times mnominal rate=EAR×m , where mmm is now 2 for semi-annual. The calculation will show that the equivalent nominal rate compounded semi-annually is approximately 4.24%.
Learning Objectives
- Understand the process of converting between different compounding intervals.