Financial Math Basics You Need to Know
What kind of math skills do you need to manage your finances? Much of the time, addition and subtraction serve you well.
There are times, though, that math specific to finance is useful. When you are facing a decision or contemplating how to improve your financial position, do the math. You'll often need to understand certain concepts and know how to do certain calculations like the ones I have included below.
Calculate Loan Payments
Before you think about borrowing money to go to college, enter into price negotiations on a car or house that you’ll finance with a consumer or mortgage loan, or put your beach trip or flat screen television on your credit card, you should know what your monthly loan payment will be. (See also: The Different Types of Loans: A Primer)
Your monthly obligation is not the only factor in making a decision (the real value of the car, house, college, etc. should play a role), but it’s a critical one. Plus, you can more readily compare the impact of variables, such as a trade-in, higher down payment, scholarship, lower interest rate, longer loan term, etc. on your monthly payment.
To calculate the loan payment, you will need the following information:
- Interest rate
- Loan term
- Loan amount
Write a formula using the PMT function in a spreadsheet:
=PMT (interest rate, number of payment periods based on the loan term, and -net present value or the current loan value)
You can also use a math formula, which can be expressed as:
Payment = Interest Rate x Loan Value /(1 - POWER(1 + Interest Rate, -Number of Payment Periods))
- A car loan with a 3% interest rate for 60 months on a loan balance of $30,000 has a monthly payment of $539.06.
- A 30-year mortgage of $200,000 with a 2% interest rate has monthly payments of $739.24.
Occasionally, your actual loan payment won’t equal the calculation's result. Factors that impact the payment include:
- Service fees added to your monthly charges
- Insurance and property taxes included in your monthly house payment
- Mortgage points, sales taxes, etc. that are added (aka capitalized) to your loan balance
Comparing expected and actual payments can help uncover any misunderstandings or discrepancies.
Understand Why Certain Loans Never Go Away
You may be surprised to see a loan balance grow rather than shrink with regular payments. Certain loan structures make it likely that the balance won't disappear easily.
Common situations in which the loan balance grows or stays the same:
- You have an interest-only mortgage loan that allows you to pay only interest on the loan for a designated period of time.
- Student loan payments are deferred but still incur interest charges, which are added to the loan balance during the deferral period.
- You take a 0% financing offer but don't pay the balance in full before a certain time frame (often 18 months) so that the deferred interest is added to the account balance.
- Your credit card company gives you a payment holiday; however, interest doesn’t take a holiday and is added to your account balance if you skip a payment.
- You add new purchases to revolving loans, like credit card loans and home equity lines, even as you make regular payments.
If the balance stays the same or grows, then the loan is not fully amortizing. Create your own schedule in a spreadsheet to see how the loan should shrink and disappear; then compare those numbers with what’s really happening.
Start with this information:
- Loan balance
- Interest rate
- Term (number of months)
Then design the spreadsheet in this way (I have used "|" to indicate separation of cells in the spreadsheet):
Month 1 | Payment | Interest (Original Loan Balance x Interest Rate/12) | Principal Paid (Payment - Interest) | Balance (Original Loan Balance - Principal Paid)
Month 2 | Payment | Interest (Previous Month’s Balance x Interest Rate/12) | Principal Paid (Payment - Interest) | Balance (Previous Month’s Balance - Principal Paid)
… and so on. For a spreadsheet example, see this DIY guide. Note that a fixed-rate, fully amortizing loan should reach a $0 balance (or close to zero) in the last month of the term.
Percentages pay a big role in making everyday financial decisions, such as:
- Determining the dollar value of a sales discount or sales-tax holiday
- Calculating tips
- Figuring out how much of your paycheck will go to your 401(k) or a charity like the United Way
- Determining what percentage of your income goes to your church (or setting a dollar amount based on 10% giving)
- Figuring out how much a raise expressed in percentages will increase your gross income in dollars
Start with the base amount (the list price of an item or your gross income, for example) and multiply by the percentage (translate the percentage into a decimal, such as 10% = .10, 3% = .03, 25% = .25). The result is the dollar amount of the sales discount, tip, contribution to your 401(k) or charitable organization, or raise.
Then, if desired, take the next step in your calculations. Figure out the exact price of the item. For example, a 20% discount on a base price of $100 will save $20, but what is the actual cost of the item? It’s $80 ($100-$20). Or, you may want to determine how much you will earn next year if you get a 4% raise on a base pay of $52,000. You'll make $2,080 more and your annual base will be $54,080.
See Compound Interest in Action
You have probably heard that compound interest is important to your future wealth. The reason is twofold:
- Exponential growth of investment values happens over many years, not immediately (which is why investing as a young adult is so strongly encouraged).
- Even small annual differences in investment growth can have significant impact over many years (which is why people are willing to take risks to earn higher returns).
You can use future value (@FV) calculations to see the big-picture impact of changes in interest rates, investment contributions, and number of years invested on wealth building. But to bring the meaning of this concept into greater focus, design a spreadsheet to show sequential, year-by-year growth. That way, you can see clearly that as the base amount increases, investment growth accelerates.
For example, consider investing $10,000 for 30 years and consistently garnering 15% return (an aggressive goal that I am using to illustrate the power of compounding). In the first year, the value moves from $10,000 to $11,500. But by year 15, annual dollar growth is now more than $10,000. Then, at year 30, the account value increases by $86,000 to more than $660,000.
Year 1: $11,500 (end of year, $10,000 + $10,000 x 15% = $11,500)
Year 2: $13,225
Year 3: $15,209
Year 4: $17,490
Year 5: $20,114
Year 15: $81,371
Year 30: $662,118
Note that if you stopped reinvesting after 20 years, then you’d have $163,665 (instead of $662,118 that requires 30 years to reach). If you experienced 12% growth annually, then you would have just a tad under $300,000 in 30 years (not $662,118 that requires 15% growth). These compounding calculations illustrate that seemingly small differences (20 years vs. 30 years or 12% vs. 15%) can make a big difference over time.
Apply the Time Value of Money to Real-Life Situations
One of the basic concepts of personal finance is the time value of money. A meaningful description comes from Investor Glossary:
Time value of money is the financial concept that deals with equating the future value of money or an investment with its present value. Time value of money explains how interest rates and time affect the value of money.
Understanding time value (and specifically knowing how to calculate future value and present value) is useful in comparing options. You may want to compare the future values of two different investment scenarios or compare the present value of a series of annual payments to a lump-sum deal. Such real-life situations may include:
- Deciding between two investment options requiring different annual investment amounts and different interest rates
- Choosing a lump sum now vs. annual income for a severance package
- Comparing the value of a government pension vs. 401(k)
- Choosing between a Traditional IRA and Roth IRA
The future value function can help you to project the value of two investment options. You can compare the difference between investing $2,000 for 10 years at 5% vs. investing $5,000 for 5 years at 4% as =FV(5%,10,-2000) vs. =FV(4%,5,-5000), or $25,156 vs. $27,082.
For scenarios in which you are comparing an immediate one-time payment with a series of payments to be received over time, use a present-value calculation. You'll need the following information:
- Annual interest rate or expected growth rate
- Number of periods that you will receive payments
- Amount of each payment
For example, if you were given a choice between getting a lump-sum payment now of $75,000 vs. receiving $20,000 per year for five years (and earning 8% each year), you could figure out the present worth of the payment streams using this formula: =PV(8%,5,-20000) = $79,854 and then compare to the present value of the lump-sum amount ($75,000) to make your choice.
Applying the time value of money allows you to take dissimilar options (apples to oranges) and convert them to like comparisons (apples to apples, present value to present value, and future value to future value).
Figure Out Your Financial Position
Addition and subtraction can be just as valuable as spreadsheet functions. You can use these basic tools to do the following:
- Figure out if you are spending less than you earn
- Calculate your net worth
To determine if you are spending less than you earn, subtract expenses from take-home income. Count monthly bills (electricity, rent or mortgage, etc.), annual bills (property taxes and insurance), and other costs that may occur on a less regular schedule (groceries, gas, and vacations). If there is money left over after you pay taxes and make investments, then you are establishing a strong financial foundation.
Basic math also allows you to calculate your net worth. Add up the value of your assets (bank balances, balance of retirement accounts, home equity, etc.) and subtract your liabilities (mortgages, student loans, etc.) to determine your overall financial position.
Looking at these numbers periodically can tell you how well you are applying financial knowledge to building wealth.
How have you applied financial math basics to making decisions? Share in the comments.