Questions: The loan below was paid in full before its due date. (a) Obtain the value of h from the annual percentage rate table. Then (b) use the actuarial method to find the amount of unearned interest, and (c) find the payoff amount. Regular Monthly Payment 433.49 APR Table Annual Percentage Rate (APR) for Monthly Payment Loans Number of Monthly Payments (n) 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% Annual Percentage Rate (APR) 10.0% 10.5% 11.0% 11.5% 12.0% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 6 1.17 1.32 1.46 1.61 1.76 1.90 2.05 2.20 2.35 2.49 2.64 2.79 2.94 3.08 3.23 3.38 3.53 12 2.18 2.45 2.73 3.00 3.28 3.56 3.83 4.11 4.39 4.66 4.94 5.22 5.50 5.78 6.06 6.34 6.62 18 3.20 3.60 4.00 4.41 4.82 5.22 5.63 6.04 6.45 6.86 7.28 7.69 8.10 8.52 8.93 9.35 9.77 24 4.22 4.75 5.29 5.83 6.37 6.91 7.45 8.00 8.55 9.09 9.64 10.19 10.75 11.30 11.86 12.42 12.98 30 5.25 5.92 6.59 7.29 7.94 8.61 9.30 9.98 10.66 11.35 12.04 12.74 13.43 14.13 14.83 15.54 16.24 36 6.29 7.09 7.90 8.71 9.52 10.34 11.16 11.98 12.81 13.64 14.48 15.32 16.16 17.01 17.86 18.71 19.57 48 8.38 9.46 10.54 11.63 12.73 13.83 14.94 16.06 17.18 18.31 19.45 20.59 21.74 22.90 24.06 25.23 26.40 60 10.50 11.86 13.23 14.61 16.00 17.40 18.81 20.23 21.66 23.10 24.55 26.01 27.48 28.96 30.45 31.96 33.47

The loan below was paid in full before its due date. (a) Obtain the value of h from the annual percentage rate table. Then (b) use the actuarial method to find the amount of unearned interest, and (c) find the payoff amount. Regular Monthly Payment 433.49 APR Table Annual Percentage Rate (APR) for Monthly Payment Loans Number of Monthly Payments (n) 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% Annual Percentage Rate (APR) 10.0% 10.5% 11.0% 11.5% 12.0% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 6 1.17 1.32 1.46 1.61 1.76 1.90 2.05 2.20 2.35 2.49 2.64 2.79 2.94 3.08 3.23 3.38 3.53 12 2.18 2.45 2.73 3.00 3.28 3.56 3.83 4.11 4.39 4.66 4.94 5.22 5.50 5.78 6.06 6.34 6.62 18 3.20 3.60 4.00 4.41 4.82 5.22 5.63 6.04 6.45 6.86 7.28 7.69 8.10 8.52 8.93 9.35 9.77 24 4.22 4.75 5.29 5.83 6.37 6.91 7.45 8.00 8.55 9.09 9.64 10.19 10.75 11.30 11.86 12.42 12.98 30 5.25 5.92 6.59 7.29 7.94 8.61 9.30 9.98 10.66 11.35 12.04 12.74 13.43 14.13 14.83 15.54 16.24 36 6.29 7.09 7.90 8.71 9.52 10.34 11.16 11.98 12.81 13.64 14.48 15.32 16.16 17.01 17.86 18.71 19.57 48 8.38 9.46 10.54 11.63 12.73 13.83 14.94 16.06 17.18 18.31 19.45 20.59 21.74 22.90 24.06 25.23 26.40 60 10.50 11.86 13.23 14.61 16.00 17.40 18.81 20.23 21.66 23.10 24.55 26.01 27.48 28.96 30.45 31.96 33.47
Transcript text: The loan below was paid in full before its due date. (a) Obtain the value of h from the annual percentage rate table. Then (b) use the actuarial method to find the amount of unearned interest, and (c) find the payoff amount. Regular Monthly Payment $433.49 APR Table \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{18}{|l|}{Annual Percentage Rate (APR) for Monthly Payment Loans} \\ \hline \multirow[t]{3}{*}{Number of Monthly Payments ( n )} & \multirow[b]{2}{*}{4.0\%} & \multirow[b]{2}{*}{4.5\%} & \multirow[b]{2}{*}{5.0\%} & \multirow[b]{2}{*}{5.5\%} & \multirow[b]{2}{*}{6.0\%} & \multirow[b]{2}{*}{6.5\%} & \multicolumn{6}{|c|}{Annual Percentage Rate (APR)} & \multirow[b]{2}{*}{$10.0 \%$} & \multirow[b]{2}{*}{10.5\%} & \multirow[b]{2}{*}{11.0\%} & \multirow[b]{2}{*}{11.5\%} & \multirow[b]{2}{*}{$12.0 \%$} \\ \hline & & & & & & & \multirow[t]{2}{*}{7.0\%} & 7.5\% & 8.0\% & 8.5\% & \[ 9.0 \% \] & \multirow[t]{2}{*}{9.5\%} & & & & & \\ \hline & \multicolumn{2}{|l|}{(2)} & 的 & & & Finan & & ge per & 00 o & Amou & Finan & & & & & & \\ \hline 6 & 1.17 & 1.32 & 1.46 & 1.61 & 1.76 & 1.90 & 2.05 & 2.20 & 2.35 & 2.49 & 2.64 & 2.79 & 2.94 & 3.08 & 3.23 & 3.38 & 3.53 \\ \hline 12 & 2.18 & 2.45 & 2.73 & 3.00 & 3.28 & 3.56 & 3.83 & 4.11 & 4.39 & 4.66 & 4.94 & 5.22 & 5.50 & 5.78 & 6.06 & 6.34 & 6.62 \\ \hline 18 & 3.20 & 3.60 & 4.00 & 4.41 & 4.82 & 5.22 & 5.63 & 6.04 & 6.45 & 6.86 & 7.28 & 7.69 & 8.10 & 8.52 & 8.93 & 9.35 & 9.77 \\ \hline 24 & 4.22 & 4.75 & 5.29 & 5.83 & 6.37 & 6.91 & 7.45 & 8.00 & 8.55 & 9.09 & 9.64 & 10.19 & 10.75 & 11.30 & 11.86 & 12.42 & 12.98 \\ \hline 30 & 5.25 & 5.92 & 6.59 & 7.29 & 7.94 & 8.61 & 9.30 & 9.98 & 10.66 & 11.35 & 12.04 & 12.74 & 13.43 & 14.13 & 14.83 & 15.54 & 16.24 \\ \hline 36 & 6.29 & 7.09 & 7.90 & 8.71 & 9.52 & 10.34 & 11.16 & 11.98 & 12.81 & 13.64 & 14.48 & 15.32 & 16.16 & 17.01 & 17.86 & 18.71 & 19.57 \\ \hline 48 & 8.38 & 9.46 & 10.54 & 11.63 & 12.73 & 13.83 & 14.94 & 16.06 & 17.18 & 18.31 & 19.45 & 20.59 & 21.74 & 22.90 & 24.06 & 25.23 & 26.40 \\ \hline 60 & 10.50 & 11.86 & 13.23 & 14.61 & 16.00 & 17.40 & 18.81 & 20.23 & 21.66 & 23.10 & 24.55 & 26.01 & 27.48 & 28.96 & 30.45 & 31.96 & 33.47 \\ \hline \end{tabular
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Solution

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Solution Steps

Solution Approach
  1. Obtain the value of h: From the APR table, find the value of h corresponding to the given APR and the number of monthly payments.
  2. Calculate unearned interest: Use the actuarial method formula to calculate the unearned interest.
  3. Calculate the payoff amount: Subtract the unearned interest from the total amount due to find the payoff amount.
Step 1: Obtain the Value of \( h \)

From the APR table, for \( \text{APR} = 6.0\% \) and \( n = 24 \) monthly payments, we find: \[ h = 6.37 \]

Step 2: Calculate the Unearned Interest

Using the actuarial method, the unearned interest is calculated as: \[ \text{Unearned Interest} = \frac{n \cdot \text{monthly payment} \cdot h}{100} \] Substituting the values: \[ \text{Unearned Interest} = \frac{24 \cdot 433.49 \cdot 6.37}{100} = 662.72 \]

Step 3: Calculate the Total Amount Due

The total amount due is given by: \[ \text{Total Amount Due} = n \cdot \text{monthly payment} = 24 \cdot 433.49 = 10403.76 \]

Step 4: Calculate the Payoff Amount

The payoff amount is calculated by subtracting the unearned interest from the total amount due: \[ \text{Payoff Amount} = \text{Total Amount Due} - \text{Unearned Interest} = 10403.76 - 662.72 = 9741.04 \]

Final Answer

\[ \boxed{ \begin{align_} h & = 6.37 \\ \text{Unearned Interest} & = 662.72 \\ \text{Payoff Amount} & = 9741.04 \end{align_} } \]

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