Final answer:
a. The finance charge in this installment agreement is $559.86. b. The total interest charged by the finance company would be $2114.59. c. Shawn should use the installment plan as it will cost him less in terms of finance charges compared to borrowing from the finance company.
Step-by-step explanation:
a. What is his finance charge in this installment agreement?
To find the finance charge, we need to calculate the total amount paid by Shawn over the course of the installment agreement. The down payment is 10% of the price of the drum set, which is $3271.00 x 0.10 = $<<3271.00*0.10=327.10>>327.10. The total amount financed is $3271.00 - $327.10 = $<<3271.00-327.10=2943.90>>2943.90.
Over 24 months, Shawn will make monthly payments of $145.99, so the total amount paid will be $145.99 x 24 = $<<145.99*24=3503.76>>3503.76.
The finance charge is the total amount paid minus the amount financed, which is $3503.76 - $2943.90 = $<<3503.76-2943.90=559.86>>559.86.
b. Instead of using the store's installment plan, Shawn can borrow $3500.00 at an APR of 6.49% from a local consumer finance company. How much total interest would the finance company charge?
To calculate the total interest charged by the finance company, we need to determine the annual interest rate and the loan term in years. The APR of 6.49% is the nominal rate convertible monthly, so the annual interest rate is 6.49% x 12 = 77.88%.
Assuming Shawn borrows the full $3500.00 and repays it over 24 months, we can use the formula for compound interest to calculate the total interest charged:
Total interest = Principal x (1 + Annual interest rate)^Time - Principal
Plugging in the values, we have:
Total interest = $3500.00 x (1 + 0.7788)^2 - $3500.00 = $3500.00 x 1.604196 - $3500.00 = $5614.59 - $3500.00 = $2114.59.
c. Should Shawn use the installment plan or borrow the money from the finance company? Explain your answer.
Comparing the finance charges, we see that the installment plan results in a finance charge of $559.86, while borrowing from the finance company would result in a total interest charge of $2114.59.
Therefore, Shawn should use the installment plan as it will cost him less in terms of finance charges compared to borrowing from the finance company.