Questions: For the following loan, find (a) the finance charge and (b) the APR. Use a TVM solver to find the APR. Sebastian purchased a tablet for 695 and will make 12 monthly payments of 60.55 each. (a) The finance charge is 31.60. (Round to the nearest cent as needed.) (b) The annual percentage rate is %. (Round to the nearest hundredth as needed.)

For the following loan, find (a) the finance charge and (b) the APR. Use a TVM solver to find the APR.
Sebastian purchased a tablet for 695 and will make 12 monthly payments of 60.55 each.
(a) The finance charge is 31.60. (Round to the nearest cent as needed.)
(b) The annual percentage rate is %. (Round to the nearest hundredth as needed.)

Transcript text: For the following loan, find (a) the finance charge and (b) the APR. Use a TVM solver to find the APR. Sebastian purchased a tablet for $\$ 695$ and will make 12 monthly payments of $\$ 60.55$ each. (a) The finance charge is $\$ 31.60$. (Round to the nearest cent as needed.) (b) The annual percentage rate is $\square$ \%. (Round to the nearest hundredth as needed.)

Solution

Solution Steps

Step 1: Calculate Total Payment

The total amount paid over the loan term is calculated as: \[ \text{Total Payment} = \text{Monthly Payment} \times \text{Number of Payments} = 60.55 \times 12 = 726.60 \]

Step 2: Calculate Finance Charge

The finance charge is determined by subtracting the principal from the total payment: \[ \text{Finance Charge} = \text{Total Payment} - \text{Principal} = 726.60 - 695 = 31.60 \]

Step 3: Calculate APR

To find the annual percentage rate (APR), we first need to determine the monthly interest rate $ r $ that satisfies the equation: \[ \text{Principal} = \sum_{n=1}^{N} \frac{\text{Monthly Payment}}{(1 + r)^n} \] where $ N $ is the number of payments (12). After solving for $ r $, we convert it to APR: \[ \text{APR} = (1 + r)^{12} - 1 \] The calculated APR is approximately $ 0.0861 $ or $ 8.61\% $ when expressed as a percentage.