Paychecks, budgets, and interest

The paycheck hits the table. Tax takes a cut. What is left is what you actually take home.

In plain words

A paycheck is sitting on the kitchen table. Wages are the dollars you got paid. Income tax is a cut taken out of those wages. Earn $400 with 10% income tax and they take 0.10 × 400 = $40. Take-home pay is what is left: $360. Sales tax is different — extra money added when you buy something. Use the tax rate stated in the question.

A budget is how you split the money that comes in: rent, food, savings, and whatever is left. Rent at 30% of $2,000 is 0.30 × 2,000 = $600.

Assets are what you own that is worth money: cash, a bike, a phone. Liabilities are what you still owe, like a loan. Net worth is one subtract: what you own minus what you owe.

A bank may pay you interest: extra money earned on savings. With simple interest, each year uses the same starting amount, called the principal. For example, $300 at 4% per year earns $300 × 0.04 = $12 each year. In 2 years it earns $24. The formula is I = p × r × t: I is interest, p is principal, r is the yearly rate as a decimal, and t is time in years.

Compound interest means previously earned interest can earn interest too. At 10% per year, $100 earns $10 in year 1, giving $110. Year 2 earns 10% of $110, or $11, giving $121. Multiplying by 1.10 keeps the full balance (100%) and adds 10%. With the same starting amount and positive yearly rate, yearly compound interest earns more than simple interest after more than one year.

Examples

Try it. Then open the steps.

Example 1 of 5

Income tax on wages

A paycheck on the kitchen table

Kim earns $350 in wages (the money she is paid). Income tax is 8% of wages — a cut taken out before she gets the cash. How much tax is taken out? What is take-home pay (what she actually keeps)?

Example 2 of 5

A monthly split

Cash in three jars

Income is $2,000. Housing is 30%, food is 15%, savings is 10%. How many dollars go to housing?

housing 30%

food 15%

save 10%

rest 45%

total $2,000

Example 3 of 5

What you own minus what you owe

A bike and a little cash

Cash $80, bike $120. Those are assets — things you own. You still owe $50 on the bike. That $50 is a liability — money you still have to pay back. Net worth is assets minus liabilities. What is your net worth?

Item	Type	Dollars
cash	asset	80
bike	asset	120
bike loan	liability	50

Example 4 of 5

Simple interest

Savings earning interest in a bank account

You save $300. The bank pays 4% simple interest for 2 years. Simple means: each year they pay 4% of the starting $300, then add those years together. In letters: I = p × r × t, where p is the starting $300, r is 0.04, t is 2 years. How much interest?

Example 5 of 5

Simple vs compound, two years

Two savings accounts, two ways to calculate interest

You put $500 in the bank at 10% per year for 2 years. Simple interest uses the starting $500 both years. Compound interest means year 2 also pays 10% on last year’s extra. Simple amount? Compound amount (starting × 1.10 × 1.10)? Which earns more, and by how much?

Things to watch for

Easy to miss: Adding income tax to your pay instead of subtracting it when finding take-home pay. Another trap is using 8% when the stated rate is 8.25%.
Do this: Income tax is percent of wages. Sales tax is percent of the price. Write 8.25% as 0.0825.
Easy to miss: Leaving r as 5 instead of 0.05 in I = prt, or using simple interest when the problem says compound.
Do this: Turn the percent into a decimal first. 5% is 0.05, not 5. Simple is I = p × r × t. Compound for 2 years is starting × (1 + r) × (1 + r).

24 problems · Camp, Trail, Summit

Practice Solution key