What is the effective annual interest rate corresponding to a nominal rate of 6% per annum compounded semi-annually________?
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Answer: D. 6.09%
Explanation
A nominal annual rate of six percent compounded semi annually yields three percent every six months. The effective annual rate is found by squaring one plus zero point zero three and subtracting one. Calculating this expression results in one point zero six zero nine minus one, which equals six point zero nine percent. Nominal interest rates state the annual rate without accounting for the frequency of compounding. Effective annual rate measures the true return on an investment over a full year with compounding. Semi annual compounding divides the nominal annual percentage rate by two for each half year period.
Lending regulations require financial institutions to disclose effective annual rates to protect borrowers. Investors compare effective rates across different savings products with varying compounding frequencies. Economic forecasting relies on effective interest metrics to analyze true borrowing and lending costs. Option A underestimates the compounding effect by treating the rate as simple annual interest. Option B represents a slight calculation error that misses the exact decimal expansion. Option C is incorrect because the precise mathematical squaring yields a nine in the final decimal place.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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