The Saving Plan: AP in Daily Life
Every month you save Rs 100 more than the previous month. After 12 months, how much total?
Equation
y = x/2 * (2*100 + (x-1)*50)
Graph
Table
| x | y |
|---|---|
| 1 | 100 |
| 2 | 250 |
| 3 | 450 |
| 4 | 700 |
| 5 | 1000 |
| 6 | 1350 |
| 7 | 1750 |
| 8 | 2200 |
| 9 | 2700 |
| 10 | 3250 |
| 11 | 3850 |
| 12 | 4500 |
What this lesson covers
What you do
You shape the function y = x/2 * (2*a + (x-1)*d) and watch the graph answer.
Challenges to clear
- Set a = 500 and d = 100: total savings after 12 months reach Rs 12,600.
- Halfway check: month 6 shows Rs 4,500 in the bank.
- A different savings plan: the first month you put away Rs 300. Slide a there.
- Now the monthly increase: after 12 months the total must be Rs 13,500. Saving more each month makes the total grow far faster than the deposit does.
Check yourself
Why is the total savings Rs 12,600 instead of just 12 × 500 = Rs 6,000?
If the monthly increase (d) was reduced to Rs 50 instead of Rs 100, how would the total savings S_12 change?
- Because the savings amount increases every month, so later months contribute more than Rs 500. — correct
- Because the formula multiplies by 2, doubling the initial amount.
- Because interest is added to the savings each month.
- Because the number of months is squared in the calculation.
- S_12 would decrease because the additional amount added each month is smaller. — correct
- S_12 would stay the same because the first month's savings (a) is unchanged.
- S_12 would increase because smaller increments are easier to maintain.
- S_12 would become zero because the progression is no longer valid.
Think about it
- Save Rs 500 the first month, Rs 100 more each month after. Total after 12 months?