Saving for a Course on a Tight Budget
A family of four has a monthly net income of R$ 2,400. Fixed costs: rent R$ 900, electricity R$ 180, bus fare R$ 240. They spend R$ 600 on food and R$ 120 on school materials. They also pay R$ 300 per month on a store loan for 5 more months. They want to take a professional course costing R$ 1,200, paid in one installment 6 months from now. They currently have R$ 150 in savings. The course cannot be split, and they do not want to borrow more. A used bicycle costs R$ 450 and would replace R$ 80 of monthly bus fare, but buying it now would use savings.
1. Calculate the family’s current monthly surplus and the amount saved after six months if nothing changes except that the loan ends after five months. Show your arithmetic and decide whether the R$ 1,200 course is affordable at month six.
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Current monthly expenses: 900 + 180 + 240 + 600 + 120 + 300 = 2,340. Surplus = 2,400 - 2,340 = R$ 60. Months 1-5: 5 × 60 = R$ 300. Month 6: the loan is finished, so expenses fall to 2,040 and surplus is R$ 360. Total surplus over six months = 300 + 360 = R$ 660. Add initial savings R$ 150: R$ 810. The course costs R$ 1,200, so they are R$ 390 short. It is not affordable at month six without changes.
2. Evaluate the bicycle idea. If the family buys it now using the R$ 150 savings plus part of one month’s surplus, will it help them reach R$ 1,200 by month six? Consider the R$ 80 monthly bus saving and the timing.
Read the worked answer
The bicycle cannot be bought now with only R$ 150 in savings and R$ 60 monthly surplus: after one month they would have at most R$ 210, still R$ 240 short of R$ 450. If they somehow bought it at the start, the R$ 80 monthly bus saving over six months would be R$ 480, so the net gain by month six would be only about R$ 30-too small and too risky. If they wait until the loan ends, the remaining time is too short for the R$ 80 saving to repay R$ 450. The bicycle does not solve the R$ 390 gap.
3. Propose a plan that reaches R$ 1,200 by month six without new borrowing. Include one spending cut and one timing change or saving rule, and show the new total.
Read the worked answer
Cut food spending by R$ 65 per month, from R$ 600 to R$ 535, for six months. That adds 6 × 65 = R$ 390. New total at month six: R$ 810 + R$ 390 = R$ 1,200, exactly enough. Keep the R$ 150 savings untouched and make the course payment before any optional spending. If a cut feels too tight, cut R$ 70 for a small buffer (R$ 1,230 total). This works without new borrowing and without relying on the bicycle.