Question
1 Assignment \( 02- \) Questions Question 1 Determine the equivalent continuous compounding rate (to two decimal places) of an interest rate of \( 17,5 \% \) per year, compounded quarterly.
Ask by Vargas Love.
Mar 21,2025 19:10
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Answer
The equivalent continuous compounding rate is approximately **17.13% per year**.
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The Deep Dive
To find the equivalent continuous compounding rate from a nominal rate that is compounded quarterly, you can use the formula:
\[ r_c = n \cdot \ln\left(1 + \frac{r}{n}\right) \]
where \( r \) is the nominal annual interest rate (in decimal form), and \( n \) is the number of compounding periods per year. For an interest rate of \( 17.5\% \) per annum compounded quarterly, \( r = 0.175 \) and \( n = 4 \). Plugging in those values:
\[ r_c = 4 \cdot \ln\left(1 + \frac{0.175}{4}\right) \]
This works out to approximately \( r_c \approx 0.1783 \), or \( 17.83\% \) when expressed as a percentage.
Thus, the equivalent continuous compounding rate is approximately \( 17.83\% \) per year.
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