Budgets, Saving and Credit
Mateo mows lawns and earns $\$240$ a month. He wants a $\$900$ laptop and already has $\$300$ saved. Where should his money go each month, and how long until the laptop is his? By the end of this page you will plan money like that, and you will know what a credit card or a loan really costs.
Income, Expenses and Budgets
A budget is a plan for your money. It starts with two numbers: what comes in and what goes out.
Expenses come in two kinds.
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Fixed expenses are the same amount every month: rent, car insurance, a phone plan, a streaming subscription.
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Variable expenses change from month to month: groceries, gas, dining out, entertainment.
When you have a deficit, you must raise income or cut expenses. A cut is often described as a percent of a category: $\text{percent cut} = \dfrac{\text{amount cut}}{\text{original amount}}$.
A monthly budget includes both fixed and variable expenses. Look at the following list of Maya's monthly expenses: Rent: $\$1,200$ Groceries: $\$350$ Car Insurance:…
A monthly budget includes both fixed and variable expenses. Look at the following list of Maya's monthly expenses:
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Rent: $\$1,200$
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Groceries: $\$350$
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Car Insurance: $\$100$
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Entertainment: $\$150$
Identify which expenses are fixed, and calculate the total amount of Maya's fixed expenses for the month.
Marcus has a total monthly income of $\$3,200$ from his job. His total monthly expenses (both fixed and variable) add up to $\$2,850$. If he puts all of the remaining…
Marcus has a total monthly income of $\$3,200$ from his job. His total monthly expenses (both fixed and variable) add up to $\$2,850$. If he puts all of the remaining money into a savings account, how much money will he save this month?
Noah is reviewing his monthly budget because he currently has a deficit of $\$100$. His expenses are: Rent: $\$1,000$ (Fixed) Car Payment: $\$300…
Noah is reviewing his monthly budget because he currently has a deficit of $\$100$. His expenses are:
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Rent: $\$1,000$ (Fixed)
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Car Payment: $\$300$ (Fixed)
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Groceries: $\$400$ (Variable)
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Dining Out: $\$150$ (Variable)
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Subscriptions: $\$40$ (Variable)
He decides to completely cancel all his subscriptions. What percentage of his "Dining Out" budget must he also cut to exactly balance his budget and eliminate the remaining deficit?
Budgeting with Percents
Many budgets are written as percents of income. Then each part is $\text{percent} \times \text{income}$.
First, income from a job: $\text{hourly wage} \times \text{hours per week} \times \text{weeks}$.
A popular guideline is the 50/30/20 rule: $50\%$ of income to needs (fixed expenses like rent), $30\%$ to wants (variable expenses like dining out), and $20\%$ to savings.
Budgets are also drawn as bars, circle graphs or $10 \times 10$ grids (each small square is $1\%$). Read the percent of each part, then multiply by the income.
Ethan works a part-time job earning $\$18$ per hour. He works $25$ hours a week. Assume there are exactly $4$ weeks in a month for his budget. If he allocates $40\%…
Ethan works a part-time job earning $\$18$ per hour. He works $25$ hours a week. Assume there are exactly $4$ weeks in a month for his budget. If he allocates $40\%$ of his monthly income to fixed expenses and $35\%$ to variable expenses, how much money does he have left over for savings each month?
The graphs above compare the growth of a $\$1,000…
The graphs above compare the growth of a $\$1,000$ deposit over time. Panel A shows simple interest, and Panel B shows compound interest. Based on the data projected on the graphs for Year 5, what is the exact difference in the account balance between the compound interest account and the simple interest account at year 5?
James follows the 50/30/20 budgeting rule, which means $50\%$ of his income should go to "Needs" (fixed expenses), $30\%$ to "Wants" (variable expenses), and $20\%$ to…
James follows the 50/30/20 budgeting rule, which means $50\%$ of his income should go to "Needs" (fixed expenses), $30\%$ to "Wants" (variable expenses), and $20\%$ to "Savings". His total monthly income is $\$5,000$. Currently, his total "Needs" amount to $\$2,800$. How much money must he cut from his "Needs" category to strictly meet the $50\%$ target of his budgeting rule?
Saving Goals and Emergency Funds
To reach a goal, you need to know how much more you need and how fast you save. This is a two-step equation: $\text{already saved} + (\text{monthly savings}) \times (\text{months}) = \text{goal}$.
Back to Mateo. He has $\$300$, saves $\$60$ a month, and wants $\$900$.
An emergency fund is savings set aside for surprises, like a lost job. If your paycheck stops, only expenses matter:
$$\text{months covered} = \frac{\text{emergency fund}}{\text{monthly expenses}}$$Olivia wants to buy a used car that costs $\$15,000$. She currently has $\$3,000$ saved in her bank account. If she is able to save $\$400…
Olivia wants to buy a used car that costs $\$15,000$. She currently has $\$3,000$ saved in her bank account. If she is able to save $\$400$ each month from her budget, how many months will it take her to save enough money to buy the car in cash?
Evelyn has an emergency fund of $\$12,000$. Her normal monthly take-home pay is $\$4,000$. Her current monthly expenses are: Rent $\$1,500$, Utilities $\$300$, Food…
Evelyn has an emergency fund of $\$12,000$. Her normal monthly take-home pay is $\$4,000$. Her current monthly expenses are: Rent $\$1,500$, Utilities $\$300$, Food $\$600$, Car Payment $\$400$, and Entertainment $\$200$.
Suddenly, Evelyn loses her job. To stretch her savings, she cuts her Entertainment budget to $\$0$ and reduces her Food budget to $\$400$. Under this new strict budget, how many full months can she pay all of her living expenses using only her emergency fund?
Assets, Liabilities and Net Worth
Your net worth tells you what you would have left if you sold everything you own and paid everything you owe.
Aaliyah has $\$600$ in savings, a phone worth $\$300$ and a bike worth $\$150$. She owes her brother $\$80$. Her assets are $600 + 300 + 150 = \$1{,}050$, so her net worth is $1{,}050 - 80 = \$970$.
Net worth can be negative. A student with $\$1{,}000$ in assets and $\$18{,}000$ in student loans has a net worth of $1{,}000 - 18{,}000 = -\$17{,}000$.
The formula can be rearranged. If you know two of the three numbers, you can find the third:
Jordan is calculating his net worth. He has $\$450$ in his savings account and owns a bicycle worth $\$250$. However, he owes his older brother $\$50…
Jordan is calculating his net worth. He has $\$450$ in his savings account and owns a bicycle worth $\$250$. However, he owes his older brother $\$50$ for a video game. Calculate Jordan's total net worth.
A family's total assets are valued at $\$5,000$. If their calculated net worth is $\$3,500$, what is the total value of their liabilities?
A family's total assets are valued at $\$5,000$. If their calculated net worth is $\$3,500$, what is the total value of their liabilities?
Review the financial information for the Smith family below: House value: $\$300,000$ Checking account: $\$3,000$ Investment account: $\$12,000…
Review the financial information for the Smith family below:
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House value: $\$300,000$
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Checking account: $\$3,000$
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Investment account: $\$12,000$
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Mortgage owed: $\$240,000$
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Student loan debt: $\$25,000$
Categorize each item as an asset or a liability, and calculate the Smith family's total net worth.
How Transactions Change Net Worth
Money moves around all the time. Some moves change your net worth and some do not. Ask: did assets or liabilities change by a different amount?
| Transaction | Assets | Liabilities | Net worth |
|---|---|---|---|
| Pay off a debt with cash | down | down by the same amount | no change |
| Buy something with cash | cash down, item up by the same amount | no change | no change |
| Buy something with a loan | up | up by the same amount | no change |
| Earn income | up | no change | up |
| Spend on living costs (food, rent, a movie) | down | no change | down |
| An item loses value (depreciates) | down | no change | down |
| An item gains value (appreciates) | up | no change | up |
Paying off a debt with cash makes you feel lighter, but your net worth stays the same. You lose $\$400$ of assets and also $\$400$ of liabilities.
William has a net worth of $\$2,500$. He has $\$800$ in his checking account and a credit card debt of $\$300$. If he uses $\$300$ from his checking account to…
William has a net worth of $\$2,500$. He has $\$800$ in his checking account and a credit card debt of $\$300$. If he uses $\$300$ from his checking account to completely pay off his credit card debt, what will his new net worth be? Explain how this transaction affects his total assets and total liabilities.
The diagram above shows a personal balance sheet. The individual has a target net worth of $\$60,000…
The diagram above shows a personal balance sheet. The individual has a target net worth of $\$60,000$. Based on the given assets and the known liabilities, calculate the exact amount owed on the Mortgage to achieve this target net worth.
At the beginning of the month, Harper's net worth is $\$10,000$. During the month, she earns $\$4,000$ in income and spends $\$3,200…
At the beginning of the month, Harper's net worth is $\$10,000$. During the month, she earns $\$4,000$ in income and spends $\$3,200$ on normal living expenses. She uses all of her remaining cash surplus to buy a new television for $\$800$. However, the television is a depreciating asset and immediately loses $20\%$ of its value the moment she buys it. Calculate Harper's exact new net worth at the end of the month.
Simple and Compound Interest
When you put money in a savings account, the bank pays you interest. When you borrow, you pay interest. Both use the same ideas.
With compound interest, interest is added to the balance each year, and next year you earn interest on the new, bigger balance. You earn "interest on interest." With annual compounding, multiply by $(1 + r)$ each year:
$$A = P(1 + r)^t$$Try different numbers in the explorer. Notice how the gap grows as time goes on.
Sarah deposits $\$800$ into a savings account that earns $5\%$ simple interest per year. If she leaves the money in the account for $3…
Sarah deposits $\$800$ into a savings account that earns $5\%$ simple interest per year. If she leaves the money in the account for $3$ years and makes no other deposits or withdrawals, how much total interest will she earn?
Isabella is comparing two different savings accounts for a $\$5,000$ deposit over $2$ years. Account A offers $4\%$ simple interest per year. Account B offers $4\%…
Isabella is comparing two different savings accounts for a $\$5,000$ deposit over $2$ years.
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Account A offers $4\%$ simple interest per year.
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Account B offers $4\%$ interest compounded annually.
Calculate the total amount of money in each account after $2$ years. How much more money will Isabella have if she chooses the compound interest account?
Lucas needs to finance a $\$20,000$ car. He is comparing two loan options: Option A: $5\%$ simple interest per year for $4$ years. Option B: $7\%…
Lucas needs to finance a $\$20,000$ car. He is comparing two loan options:
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Option A: $5\%$ simple interest per year for $4$ years.
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Option B: $7\%$ simple interest per year for $3$ years.
Calculate the total cost of the car (principal plus interest) for each option. Which option is cheaper overall, and by how much?
Credit Cards and APR
A credit card lets you spend money you do not have yet. The card company lends it to you. A debit card is different: it takes money from your own checking account.
What you owe is the balance. If you do not pay it off, the company charges interest. The yearly rate is the APR (Annual Percentage Rate). Interest is charged every month, so:
$$\text{monthly rate} = \frac{\text{APR}}{12} \qquad \text{interest} = \text{balance} \times \text{monthly rate}$$Each month you must pay at least the minimum payment. Many cards use "the greater of a fixed amount or a percent of the balance". The payment first covers interest. Only what is left reduces the principal (the amount you borrowed).
Chloe has a credit card balance of $\$500$. Her credit card company requires a minimum monthly payment of either $\$25$ or $4\%$ of the total balance, whichever is…
Chloe has a credit card balance of $\$500$. Her credit card company requires a minimum monthly payment of either $\$25$ or $4\%$ of the total balance, whichever is greater. Calculate $4\%$ of her balance and determine the minimum payment she must make this month.
Jackson has a credit card with a balance of $\$1,200$ and an Annual Percentage Rate (APR) of $18\%$. To find the monthly interest rate, divide the APR by $12…
Jackson has a credit card with a balance of $\$1,200$ and an Annual Percentage Rate (APR) of $18\%$. To find the monthly interest rate, divide the APR by $12$. If Jackson makes no new purchases and pays off exactly the interest charged for the first month, how much money will he pay in interest?
Sophia has a credit card balance of $\$2,000$ with an APR of $24\%$. Her credit card company requires a minimum payment of $\$60$ this month. First, calculate the…
Sophia has a credit card balance of $\$2,000$ with an APR of $24\%$. Her credit card company requires a minimum payment of $\$60$ this month.
First, calculate the monthly interest rate, and find out how much of her $\$60$ payment will go toward paying interest. Then, calculate how much will actually go toward reducing the principal balance, and determine her new balance after making the minimum payment.
Fees and the True Cost of Borrowing
Borrowing costs more than the interest. There can be fees too: an overdraft fee when you spend more than your checking account holds, an activation fee, or an upfront fee on a cash advance. To compare choices, find the total cost of each one and compare.
For example, a $\$12$ purchase with only $\$8$ in your account and a $\$30$ overdraft fee really costs $12 + 30 = \$42$. A $\$400$ TV with a store card gives $15\%$ off but has a $\$30$ fee: the cost is $400 \times 0.85 + 30 = 340 + 30 = \$370$, which is $\$30$ less than paying cash.
With loans over several years, the lower rate is not always the cheaper loan. Time matters too.
Liam wants to buy a new video game that costs $\$50$. He only has $\$40$ in his checking account. If he uses his debit card to buy the game, his bank will charge him a…
Liam wants to buy a new video game that costs $\$50$. He only has $\$40$ in his checking account. If he uses his debit card to buy the game, his bank will charge him a $\$35$ overdraft fee. What will be the total cost of the game if he chooses to use his debit card and incur the fee?
Mia wants to buy a new laptop priced at $\$900$. The electronics store offers her their store credit card, which gives a $10\%…
Mia wants to buy a new laptop priced at $\$900$. The electronics store offers her their store credit card, which gives a $10\%$ discount on the laptop but charges a one-time $\$50$ activation fee. Alternatively, she can pay with cash for the full price. Which payment method is cheaper, and by how much?
Daniel needs $\$500$ immediately for a car repair. He has two choices to borrow the money for one month: Choice 1: A payday loan that charges a flat fee of $\$75$.…
Daniel needs $\$500$ immediately for a car repair. He has two choices to borrow the money for one month:
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Choice 1: A payday loan that charges a flat fee of $\$75$.
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Choice 2: A credit card cash advance that charges a $3\%$ upfront fee on the amount borrowed, plus an APR of $24\%$ (which equals $2\%$ monthly interest applied to the original borrowed amount).
Calculate the total cost of borrowing the money for one month using each choice. Which option is cheaper, and by how much?
Summary
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Budget: income minus expenses. Positive is a surplus (savings), negative is a deficit. Fixed expenses stay the same; variable ones change. The 50/30/20 rule splits income into needs, wants and savings.
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Saving goals: solve $\text{saved} + \text{monthly} \times \text{months} = \text{goal}$ (round up). Emergency fund months $= \text{fund} \div \text{monthly expenses}$ (round down for full months).
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Net worth $= \text{assets} - \text{liabilities}$. Paying a debt with cash or buying an asset with cash does not change it. Income raises it, spending on living costs and depreciation lower it.
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Interest: simple $I = Prt$; compound $A = P(1 + r)^t$. Use the rate as a decimal and the time in years.
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Credit: monthly rate $= \text{APR} \div 12$. A payment covers interest first, the rest reduces the balance.
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Compare options by total cost: price, fees, interest and discounts all together.