Choosing a Payment Plan Under Constraints
A student needs to buy a used laptop for a coding course. The laptop costs 720 euros. She has 200 euros saved and can set aside 60 euros per month from a part-time job. The store offers two plans. Plan A: pay the full price at purchase and receive a 10 percent discount. Plan B: pay a 50-euro deposit now, then 70 euros per month for 10 months, with no discount. She must have the laptop before the course starts in 4 months. She cannot borrow money, and any plan must be fully paid before she may take the laptop home under store policy.
1. Determine whether she can afford Plan A within 4 months, and whether Plan B is feasible under the store's policy.
Read the worked answer
Plan A: the discount is 10 percent of 720, or 72 euros, so the price is 720 - 72 = 648 euros. She has 200 now and saves 60 per month. In 4 months she adds 4 x 60 = 240, giving 200 + 240 = 440 euros. That is less than 648, so she cannot pay in full within 4 months. Plan A is not feasible on time.
Plan B: she pays 50 now, leaving 720 - 50 = 670 euros, repaid at 70 per month over 10 months (70 x 10 = 700, which covers the balance and includes 30 euros of financing cost). But store policy requires full payment before taking the laptop home, and she needs it in 4 months. After 4 months she would have paid only 50 + 4 x 70 = 330 euros, far short of 720. So Plan B is also infeasible under the policy, despite the smaller monthly burden.
2. She can increase her monthly savings. What minimum monthly amount lets her use Plan A within 4 months, and how does that compare with Plan B's monthly requirement?
Read the worked answer
For Plan A she needs 648 euros total. She already has 200, so she must save 648 - 200 = 448 euros over 4 months. That requires 448 / 4 = 112 euros per month.
Plan B requires 70 euros per month for 10 months plus the 50-euro deposit, but it takes 10 months to complete, which violates the 4-month deadline regardless of monthly amount. To finish Plan B in 4 months she would need to repay 670 euros over 4 months, or 167.50 euros per month, plus the deposit.
So Plan A at 112 euros per month is both cheaper overall (648 versus 720) and requires less monthly saving than compressing Plan B into 4 months (167.50). The judgment: if she can raise her savings to 112 per month, Plan A is clearly superior. If she cannot, neither plan meets the deadline, and she should consider a cheaper laptop or delaying the course.