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Saving for College

Saving for college is a math problem with three parts: how much do steady deposits add up to, how much does interest add on top, and what fraction of the bill does that cover? Each part is a skill you already have — multiplication, the interest formula, and percents — pointed at one big goal.

The engine of every savings plan is consistency. A modest amount saved every month, started early, grows into a serious number, because months pile up fast: four years is 48 deposits, not four.

Total up the monthly deposits

Steady saving follows one formula: total saved=monthly amountmonths\text{total saved} = \text{monthly amount} \cdot \text{months}. The only trap is the units — savings problems usually give the time in years, and the formula needs months. Since 1 year is 12 months, 3 years is 312=363 \cdot 12 = 36 months and 4 years is 48.

So saving $150 a month for 4 years gives 15048=7200150 \cdot 48 = 7200 — $7,200. Skip the conversion and multiply by 4 instead of 48, and your answer comes out twelve times too small. That wrong answer is on almost every multiple-choice list.

Starting early is what makes the multiplication work for you. Every extra year adds 12 more deposits, and it gives interest more time to help.

Let interest help

Money you have already saved can earn interest while it waits. At 5% simple interest, $7,200 earns I=72000.052=720I = 7200 \cdot 0.05 \cdot 2 = 720 over 2 years, growing the fund to $7,920 without a single extra deposit.

Interest never replaces saving — it rewards it. The bigger the balance you build with deposits, the more the interest adds on top.

What percent of the cost is covered?

The last question a savings plan answers is how far it goes: divide the amount saved by the total cost, then convert to a percent. If one year of college costs $12,000 and you have saved $9,000, then 900012000=0.75\dfrac{9000}{12000} = 0.75, which is 75%75\% of the cost.

The saved amount always goes on top of the fraction. A percent under 100 means there is still a gap to close; the plan tells you exactly how big it is.

Worked examples

Example 1: total saved over time

You save $95 a month for 2 years. How much do you save in all?

Convert years to months212=242 \cdot 12 = 24
Multiply by the monthly amount9524=228095 \cdot 24 = 2280

Answer: You save $2,280 in all.

Example 2: savings plus interest

You move $4,000 of savings into an account paying 3% simple interest for 2 years. Find the new balance.

Find the interestI=40000.032I = 4000 \cdot 0.03 \cdot 2
MultiplyI=240I = 240
Add it to the savings4000+240=42404000 + 240 = 4240

Answer: The new balance is $4,240.

Example 3: percent of the cost covered

Diego saves $250 a month for 4 years. One year of college costs $15,000. What percent of that cost will his savings cover?

Convert years to months412=484 \cdot 12 = 48
Find the total saved25048=12000250 \cdot 48 = 12000
Divide saved by cost1200015000=0.8\dfrac{12000}{15000} = 0.8
Convert to a percent0.8=80%0.8 = 80\%

Answer: His savings cover 80%80\% of one year of college.

Try one yourself

Common questions

Why do I have to convert years to months?

Because the deposits happen monthly, so the formula counts months. One year holds 12 deposits, so multiply the years by 12 first: 3 years is 36 months. Multiplying by the number of years alone makes the total twelve times too small.

Which number goes on top when I find the percent?

The amount saved. Percent covered is savedcost\dfrac{\text{saved}}{\text{cost}}, converted to a percent. If you have saved $4,800 toward an $8,000 program, that is 48008000=0.6=60%\dfrac{4800}{8000} = 0.6 = 60\%.

Does starting early really matter that much?

Yes — twice over. Every extra year adds 12 more deposits to the total, and it gives the balance more years to earn interest. The same monthly amount started two years earlier simply ends bigger.

What if my savings grow by the same amount every year in a table?

Then the pattern is linear: find the yearly jump and extend the table one row at a time. If the total grows by $1,200 each year and year 4 shows $4,800, year 5 will show $6,000 and year 6 will show $7,200.

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