(a) Obtain the value of \( h \) from the annual percentage rate table.
Value of \( h \) for APR of \( 9.0\% \) and remaining payments of \( 6 \).
From the problem statement, we have \( h = 5 \).
\(\boxed{h = 5}\)
(b) Use the actuarial method to find the amount of unearned interest.
Calculate the total interest that would have been paid over the life of the loan.
The total interest is given by \( \text{total interest} = 349.07 \times 6 \times \left(\frac{0.09}{12}\right) = 15.70815 \).
Calculate the interest that has already been paid.
The interest paid is \( \text{interest paid} = 349.07 \times \left(\frac{0.09}{12}\right) \times (12 - 6) = 15.70815 \).
Determine the unearned interest.
The unearned interest is calculated as \( \text{unearned interest} = \text{total interest} - \text{interest paid} = 15.70815 - 15.70815 = 0.0 \).
\(\boxed{\text{Unearned Interest} = 0.00}\)
(c) Find the payoff amount.
Calculate the remaining balance of the loan.
The remaining balance is \( \text{remaining balance} = 349.07 \times 6 = 2094.42 \).
Calculate the payoff amount.
The payoff amount is given by \( \text{payoff amount} = \text{remaining balance} - \text{unearned interest} = 2094.42 - 0.0 = 2094.42 \).
\(\boxed{\text{Payoff Amount} = 2094.42}\)
The final answers are:
\( h = 5 \)
Unearned Interest = \( 0.00 \)
Payoff Amount = \( 2094.42 \)