Lisa bought a home with an adjustable-rate mortgage. The margin on the loan is $$ 4.2 \% $$ and the rate cap is $$ 5.75 \% $$ over the life of the loan. If the current index rate is $$ 6.6 \% $$, what is the calculated interest rate of the ARM? Select one: a. $$ 9.5 \% $$ b. $$ 10.8 \% $$ c. $$ 6.75 \% $$

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1. The general formula for an adjustable-rate mortgage (ARM) is:
   $$
   \text{Calculated Interest Rate} = \text{Index Rate} + \text{Margin}
   $$

2. Given:
   $$
   \text{Index Rate} = 6.6\%
   $$
   $$
   \text{Margin} = 4.2\%
   $$

3. Substitute the given values into the formula:
   $$
   \text{Calculated Interest Rate} = 6.6\% + 4.2\% = 10.8\%
   $$

4. The rate cap of $$ 5.75\% $$ over the life of the loan means the interest rate cannot exceed the initial rate by more than $$ 5.75\% $$. However, in this case, the addition of the margin and the current index rate results in $$ 10.8\% $$, which is within the allowed limit under normal circumstances, hence no further adjustment is needed.

5. Therefore, the calculated interest rate of the ARM is:
   $$
   10.8\%
   $$

The correct answer is b. $$ 10.8\% $$.
The calculated interest rate of the ARM is $$ 10.8\% $$.

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