Question

The Greens want to put an addition on their house 18 months from now. They will need to save $10,620 in order to achieve this goal. They set aside the same amount each month, and after a year discover they have saved $6,120. The Greens must adjust their plan in order to meet their goal, so they came up with the following options:
Option A: Stay with saving the original amount each month but put the addition on one month later than originally planned.
Option B: Increase the amount of money they save each month by $120 from their original plan.
Which of the following statements is true?
a.
Only option A will allow them to meet their goal.
b.
Only option B will allow them to meet their goal.
c.
Both options A and B will allow them to meet their goal.
d.
Neither option A nor option B will allow them to meet their goal.

Answer 1

Let the original monthly amount be m. From the year’s savings: 12m = 6,120 → m = 510.

They need 10,620 − 6,120 = 4,500 more.

Option A: Delay one month → 7 months left at $510 → 7·510 = 3,570. Total = 6,120 + 3,570 = 9,690 < 10,620 (short).

Option B: Increase by $120 → new monthly = 510 + 120 = 630 for the remaining 6 months → 6·630 = 3,780. Total = 6,120 + 3,780 = 9,900 < 10,620 (short).

So neither option reaches the goal. Answer: d.