What is the effective annual interest rate for a nominal rate of 6% per annum payable semi-annually:_______?
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Answer: D. Rs 6.09%
Explanation
Semi annual compounding divides the nominal annual interest rate by two for each compounding period. The effective annual rate formula squares the semi annual growth factor and subtracts one. Computing this expression results in an effective annual rate of six point zero nine percent. Nominal interest rates do not reflect the compounding frequency effects within a single year. Effective annual rates account for interest earned on previously accumulated interest periods. Compounding semi annually means interest is calculated and added to the balance every six months.
Consumers use effective annual rates to compare loans and investments with different compounding frequencies. Banking regulations often require lenders to disclose effective annual percentages for transparency. Financial planning relies on accurate interest conversion formulas to project accurate returns. Option a suggests six point zero six percent which underestimates the compounding growth effect. Option b proposes six point zero seven percent due to a minor rounding error in calculation. Option c underestimates the effective rate by one basis point compared to the exact formula.
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- Mathematics
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- Mathematics
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- —
- Difficulty
- medium
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