# Financial Math Basics You Need to Know

By Julie Rains on 16 August 2012 10 comments

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))

For example,

• 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.

• Loan balance
• Interest rate
• Term (number of months)
• Payment

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.

### Figure Percentages

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:

1. Exponential growth of investment values happens over many years, not immediately (which is why investing as a young adult is so strongly encouraged).

2. 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:

1. Figure out if you are spending less than you earn
2. 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.

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It never fails to amaze me how many people don't understand basic maths / common sense. This becomes obvious when you consider how many people are putting money away in a 2% interest savings account instead of using it to make overpayments on a mortgage being charged at 4% interest!

Thanks for your comment. I think that seeing the impact of financial decisions can help people make more informed choices.

There may be other factors in play (such as the desire to have a cash balance rather than higher home equity or quicker payoff, or a desire to minimize risk rather than go for greater returns) but it is helpful to make these decisions with a broader understanding.

What do you expect, kids learn from a young age that it's all right to hate math. A lot of kids get lost around division/fractions, and sadly if they don't comprehend those well the intuitiveness of basic math goes out the window. Sure they may make it through linear algebra, and even a good chunk of pre-calc by memorizing formulas, but they can never put math to practical use because they don't realize how it all really "works."

Then there is the battle of the mind. Some people are logical and some people are emotional. It feels good to eat nice food, and put \$200 in the bank - instant gratification - and after a couple of months they can buy a new TV/Computer/whatever.

Logical people know the math and realize that the long-term reward that you mentioned is worth it.

Emotion and naivety are two hard things to battle my friend, and that's why all of nature falls back on the bell curve. Some people are just destined to be a certain way.

You are correct in your statement I receive a bonus (bi-monthly) and I do make an overpayment on my mortgage of 17%, my fear is that I cannot make up for not saving enough in the past. At 55 years of age it is an up hill climb, and I know how some times we just do not make enough income.

Thanks I love the aviator

James

Great article! I'm certain that too many people really don't get the concept of debt, how it works, how much it's costing them, etc. The bigger picture is, too many people are socking money away in savings or investments, while at the same time paying double-digit rates on credit card debt!

You don't understand the concept of taxation and time value of money. If I put 3% of my paycheck into my 401k and my employer matches 3% (automatic 3% raise for doing nothing!!!) and I avoid 15% taxation and the historical average yearly return on the stock market is 9.4% I get 3+9.4+5.0 (the 5.0 is derived from me assuming I will be in the 10% or less tax bracket when I retire (politics aside) and pull the money out) So I get a 17.4% return on my money in my 401k verses my highest credit card rate of 14.5% with my average being 11.50%= So by putting my money in my retirement account instead of quickly paying off my credit cards I'm actually ahead by 5.9%. I guess that MBA has paid off!

Nice. I especially relate to the time value of money concept. If people would learn at an early age to start earning interest or returns and let them compound over time, we'd all have a lot less financial problems. Of course it all starts with calculating how much of your paycheck you can put away.

Awesome article! I think this kind of information will be very helpful for people who come across it and don't know how to calculate figuring out certain loan payments like this. Some of these formulas really would have helped when I was figuring out which student loans to get in comparison to others and how long they would take to pay off.

"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"

This statement sums the very core of this article. There are many individuals try to get a loan (for whatever purpose) but they are not really aware how to make their payments easier and more practical. They simply "nod" to banks and these financial institutions without really understanding what is going on with regards to interests and what not's. One of the easiest thing to do is to get some debt consolidation service for an informed option.

These are basic formulas that anyone looking to build a substantial net worth should understand inside out. Unfortunately, the only time you actually learn them is if you were a finance or economics major or if you took the time to learn about personal finance yourself. Isn't it amazing how they don't teach basic money management in high school or college?