Final answer:
Paul's loan contract stipulates a 12.4% interest compounded monthly. To determine how much extra Paul pays for the 'buy now and pay later' option, we calculate the total amount paid over 18 months ($2,052) and subtract the cash price of the sound system ($1,500), resulting in an extra $552 paid.
Step-by-step explanation:
Paul's Sound System Loan Analysis
When determining the nominal monthly interest rate during the payment period for Paul's car sound system, it is necessary to consider the nature of the contract. The contract stipulates a monthly compounded interest, which means that interest is added to the principal balance each month. In general, the formula to convert an annual nominal interest rate to a monthly one is to divide by 12, as interest rates are typically annual rates.
However, for this question we are already given that for the first year, there is a 12.4% compounded monthly interest rate. This rate translates directly to a monthly rate of 1.033% (12.4% รท 12). However, after the first year, when Paul starts making payments, the contract does not specify the interest rate. If the same rate is assumed, the equation for monthly payments can be used to find the present value of the loan at the beginning of the repayment period, but this was not asked for and would require additional information.
To calculate the total amount Paul would pay over the contract term, we sum the total payments made during the repayment period. Paul pays $114 per month for 18 months, totaling $2,052. The extra amount paid is the difference between this total and the cash price: $2,052 - $1,500 = $552. Thus, Paul would pay an extra $552 for the convenience of the "buy now and pay later" option.