When the effects and impacts of compounding over time are taken into account, the effective annual interest rate is the true return on a savings account or any other interest-paying investment.
Option C is the correct answer: Loan F's effective rate will be 0.302 percentage points lower than Loan G's.
The interest rate on loan F is 5.66 percent per month, compounded.
The interest rate on loan G is 6.02 percent, compounded semi-annually.
[tex]\text{Effective rate for loan F}:\\\\r = 1+\frac{0.0566}{12}^{12} - 1 \\\\\n=12\\\\\\text{or}\\\\\r=0.0580916\\\\\\\text{Effective rate for loan G}\\\\r = 1+\frac{0.0602}{12}^{2} - 1 \\\\\\n = 2\\\text{or}\\\\\r=0.0611106\\\\\\\text{ The difference between the loans for G and F}:\\\\=0.061106-0.058091\\\\=0.00302\\\\\text{or}\\\\=0.00302 \text{ x } 100\\\\=0.302 \text{percent}[/tex]
Therefore, option c is the correct answer.
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