Question

Darla purchased a new car during a special sales promotion by the manufacturer. She secured a loan from the manufacturer in the amount of $23,000 at a rate of 7%/year compounded monthly. Her bank is now charging 11.3%/year compounded monthly for new car loans. Assuming that each loan would be amortized by 36 equal monthly installments, determine the amount of interest she would have paid at the end of 3 yr for each loan. How much less will she have paid in interest payments over the life of the loan by borrowing from the manufacturer instead of her bank? (Round your answers to the nearest cent.)

interest paid to manufacturer	$
interest paid to bank	$
savings	$

Answer 1

Manufacturer Loan: Interest Rate = 7 %, Compounding Frequency: Monthly

Amount = $ 23000, Number of Equal Installments = 36

Let the equal monthly installments be $ m

Applicable Monthly Interest Rate = 7/12 = 0.5833 %

Therefore, 23000 = m x (1/0.005833) x [1-{1/(1.005833)^(36)}]

23000 = m x 32.386656

m = 23000 / 32.386656 = $ 710.17

Bank Loan: Interest Rate = 11.3 %, Compounding Frequency: Monthly

Amount = $ 23000, Number of Equal Installments = 36

Applicable Monthly Interest Rate = 11.3 / 12 = 0.94167 %

Let the monthly repayments be $ n

Therefore, 23000 = n x (1/0.0094167) x [1-{1/(1.0094167)^(36)}]

23000 = n x 30.412712

n = 23000 / 30.412712 = $ 756.26272 ~ $ 756.26

Total Interest Paid in Manufacturing Loan = m x 36 - 23000 = 710.17 x 36 - 23000 = $ 2566.08

Total Interest Paid in Bank Loan = n x 36 - 23000 = 756.26 x 36 - 23000 = $ 4225.46

Additional Interest Paid = 4225.46 - 2566.08 = $ 1659.37