Problem
Karen and Wayne need to buy a refrigerator because theirs just broke. Unfortunately, their savings account is depleted, and they will need to borrow money in order to buy a new one. Sears offers them an installment loan at $10 \%$ (add-on rate). If the refrigerator at Sears costs $\$ 1,540$ plus $5 \%$ sales tax, and Karen and Wayne plan to pay for the refrigerator for 4 years, what is the monthly payment? (A) $\$ 47.16$ (B) $\$ 35.45$ (C) $\$ 44.92$ (D) $\$ 51.88$
Solution
Step 1 ：First, calculate the total cost of the refrigerator including the sales tax: \(1540 \times (1 + 0.05) = 1617.0\)
Step 2 ：Next, calculate the total amount of the loan including the interest: \(1617.0 \times (1 + 0.1 \times 4) = 2263.8\)
Step 3 ：Finally, divide the total amount of the loan by the number of months in 4 years to get the monthly payment: \(2263.8 \div 48 = 47.1625\)
Step 4 ：The monthly payment is approximately \(\boxed{47.16}\)
