financial calculations

Financial Math Basics You Need to Know

Julie Rains — Thu, 16 Aug 2012 10:36:42 +0000

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.

Start with this information:

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:

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.

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This article is from Julie Rains of Wise Bread, an award-winning personal finance and credit card comparison website. Read more great articles from Wise Bread:

How to Calculate Future Value, and Why It Matters

Julie Rains — Wed, 01 Aug 2012 10:24:41 +0000

I love financial functions on spreadsheets, and one of my favorites is @FV. This function enables you to calculate the future value of a stream of payments. You have to make assumptions about interest rates, but you can use the function to project the value of investments. For example, a simple-to-make formula lets you know that if you set aside $2,000 per year for 10 years and earn 5% each year, you'll have $25,000 at the end of the term. (See also: Investing 101: 5 Essential Steps)

Where to Find Future Value (@FV) Functions

You'll find @FV available in spreadsheets from Microsoft (Excel), Google Drive (or its predecessor Google Docs), Open Office, and more. Look for financial and other types of functions on the toolbar under "Insert" or the icon that looks like an E. I particularly like Microsoft's version because there are prompts embedded in the function that help me write the formula.

How to Write an @FV Formula

To create a formula that calculates future value, put in a series of numbers based on your best estimate. In Excel, the formula is @FV (rate, nper, pmt, [pv], [type]). Here's what those abbreviated words and acronyms mean:

Rate

The rate is the interest rate or investment return that you'll earn over the life of the investment. You can enter this number in a couple of ways. For example, 6% annual rate could be entered as 6% or .06. Note that if you are making payments monthly or quarterly, then you would need to divide the interest rate by 12 (months) or 4 (quarters). Enter .06/12 for monthly payments; .06/4, quarterly payments.

NPER

NPER is the number of time periods in which you will make payments or contributions. For example, if you are planning on contributing $2,000 to a Traditional IRA, Roth IRA, or SEP-IRA for 20 years, then the number of periods equals 20. However, if you are contributing $300 monthly to a 401(k) over 20 years, then the number of periods is 20 (years) X 12 (months) = 240. (Remember to divide your interest rate by the number of periods if you are making contributions periodically during the year; the interest rate for the 401(k) formula would be .06/12, which is the interest rate divided by number of months).

PMT

This number is the fixed payment or contribution made without fail over the number of periods specified.

This number is the present value, upfront contribution, or the starting balance of the investment.

Typically, when I do future value calculations on a stream of payments, I use "0" (that is, zero) as the present value because the account is new and has no value yet. But, in reality, you often start saving with a base amount (see my calculations of the future value of current retirement savings in How Much Money Will You Need to Retire? spreadsheet). For example, you can calculate the future value of your 401(k) in 20 years based on a 5% interest rate, annual contribution of $3,000, and amount that you have amassed in the account. If the account value is $12,000 now, then the formula is @FV (5%,20,-3000,-12000,0) = $131,037.

Note that you can omit the present value altogether if the starting account balance is zero.

Type

The type references the timing of payments or contributions. This entry is optional, and I usually put this value as "0" (zero) for simplicity's sake. But you are supposed to put "0" if the contribution or payment will be made at the end of the period (for example, December 31, 2012) and "1" if you make the contribution at the beginning of the year (for example, January 1, 2012) as interest will accrue and investment gains will presumably be made throughout the year if you start earlier rather than later.

Do the calculations both ways to see the difference. For example, if you save $5,000 yearly for 25 years and earn 5% but start at the beginning of the year (type = 1), then the future value is over $250,000, but if you wait until the end of the year to invest (type = 0), then the value grows to $238,635.

Why Calculating Future Value Matters

You may want to know what the value of your savings and investments will be worth in the future. In my article Mindless Ways to Save a Million, I illustrated how various account balances could grow over a working lifetime through automatic savings, such as direct deposits, drafts, automated investments, and regular contributions. Specifically, I looked at how the following types of accounts may grow:

Regular savings
401(K)
IRA (Traditional or Roth)
SEP-IRA (IRA for self-employed individuals)
HSA (tied to a high-deductible health plan)

You will likely experience varying rates of interest and investment returns on these accounts. For illustration purposes, I calculated future value using interest rates and investment returns that ranged from 1% to 8%. If you make regular deposits to these accounts over 30 years (in amounts ranging from $100 per month to $8,000 per year) and don't cash them out, then you can expect to save more than $1.5 million.

The difficult aspects of this scenario are:

Investing without fail over a period of 30 years
Earning high enough investment returns consistently

Nevertheless, formulas using the @FV function show the potential for future value. So, if you want to know whether saving X amount each year is really worth it, use the future value function to help you make a decision.

Do you use the @FV to calculate possibilities? How has this formula shaped your decisions?

This article is from Julie Rains of Wise Bread, an award-winning personal finance and credit card comparison website. Read more great articles from Wise Bread:

Running the numbers on the bigger car: what’s your cost and is it worth it?

Julie Rains — Mon, 21 May 2007 19:17:25 +0000

I got to ride in a new car, complete with satellite radio and new car smell, yesterday. Prompted by high gas prices, my friend traded in her SUV for a mid-size sedan. Equipped with capabilities to haul camping gear, bicycles, and perhaps kayaks, the vehicle was nonetheless deemed unsuitable for a jaunt to the mountains (hard to handle on those endlessly curving roads) or to the water park (the interior might get wet).

Until just recently, people (my friends included) most likely have thought I was either not so bright or way too broke for anything besides my straight-drive Toyota Corolla. I have continually found this befuddling as many of my friends lived through the gas crisis of the 70s (you may have studied it in history class but if you haven’t, please know that gas was rationed right here in the United States of America) and seem at least vaguely aware of global warming. I’d like to claim a purely environment platform but here’s my rationale: I hate to spend money when I don’t have to.

Okay, let’s do the math:

Ford Explorer

Cost: $26,105
Monthly Payment: $525.58 (60-month, 7.7% loan, calculate it yourself using the PMT-Payment function in Excel or go to www.bankrate.com)
Fuel cost per month: $195.75 (estimate per www.edmunds.com)

Toyota Corolla

Cost: $15,350
Monthly Payment: $309.04
Fuel cost per month: $96.67

The monthly difference ($315.62) is called the utility cost and you need to decide whether the increased pleasure is worth the expense. But know that if you buy the Corolla, invest the difference in the stock market (and earn 10% annually), then at the end of five years, you will be $24,644.36 richer (I used the FV-Future Value function in Excel).

Hmm… you could even pay cash for your next car.

This article is from Julie Rains of Wise Bread, an award-winning personal finance and credit card comparison website. Read more great articles from Wise Bread: