Maths can save you money
This is one in an occasional series on maths for consumers:
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Making Sense of Cents and Percent. Even though we hate to admit it, for most of us, including me, it has been a long time since we really thought about these pesky math concepts such as reciprocals, compounding, finding X when you know Y, present value, annuities, and square roots.
Did any of us really think that we would use any of that stuff once we got out of school? If you were like me, you walked out and never looked back.
In hindsight, I wish I had truly understood how maths could help me in everyday life. However, falling into a typecast clich?, I was like most ladies where maths was a daunting task with little relevance linking school maths to real-time consumerism.
Readers are often surprised to hear that their financial advisor could have (and ignore) math anxiety. But the day of reckoning came. If I was going to pursue a career where I had to pass complex professional qualification exams (with tons of maths problems) and then advise clients on financial issues, this anxiety had to be alleviated. I went to the extreme and hired a maths tutor.
As consumers and employees/employers, we are exposed to maths computations every day in our personal and our business lives: every time we stand in line at a bank to convert Bermuda dollars into something else; review the adjustable rate on our mortgages; decipher price increases on food items weighed in grams or pounds and ounces; compare the differences on certificates of deposit rates; understand the minimum monthly payment on a credit card bill; or, consider trading gains and losses on an investment portfolio.
If a business owner is not comfortable with mark-ups, markdowns, breakeven, and computing the real profit margin particularly when running a line of credit, the end result somewhere down the line can be a tremendous disappointment, or worse.
Recent survey in both the UK and the US indicate that more than 40 percent of average consumers do not take the timetounderstand compound interest, or to compare discounted prices between two choices of retail items, such as cars.
Here are a few refreshers on ways to think about your money. If this is simply too taxing for your brain, then go to http://www.360financialliteracy.org and use their calculators.
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Compound interest: Let?s say your savings account can compound under the following offerings ? 6% interest on a $1,000 fixed deposit, compounded daily, compounded monthly, compounded quarterly, and paid once a year. Can you figure out which is the better deal?
The first challenge is, which number to use. Do I take the 1,000 (the principal) and multiply it by 6% (.06 the interest rate) and add it to the principal for a princely sum of $1,060? That works doesn?t it? Sure, that is simple interest for one year. But, will I earn more if it compounded more frequently? Of course!
Each bit of interest is added to the principal for each period and the total amount (both interest and principal) is recalculated again.
Compounding monthly works like this:
Figure out the monthly rate of interest by dividing the annual rate by twelve (.06 divided by 12 months) = .005 interest rate per month
Multiply the first month principal $1,000 times .005 = $5 interest earned for the first month. Add to the principal = $1,005
Second month = your principal is now $5 more = 1,005
Multiply $1,005 by .005 = $5.03 notice that the second month you earned more interest than the first. Add that interest to first month principal total = $1,010.03
Third month = 1,010.03 times .005 interest = 5.05 and add that to your principal. 1,015.08
And so on for each month, keep adding the new increasing interest to the accumulating principal until you reach one year. Compare the total amount of paying interest only once a year to paying interest (and compounding once a month)
Challenge - now see if you can compound your principal daily.
Start with dividing your annual interest rate of 6% (0.06) by 365 days = 0.0002 per day. The second challenge is keeping track of all those decimals! A calculator helps.
As you can see, the more frequent the compounding period, the higher the amount of interest you can earn. Choosing daily compounding if offered by your financial institution, therefore, will earn you the highest effective rate of interest in a year.
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By contrast, credit card balances do the same thing, with one catch - Minimum credit card payments.
Let?s take the same example as before in compounding your savings, but turn it upside down. Note that your credit card provider is earning the interest, not you.
Your interest rate is 18 percent (0.18 divided by 12) a year, therefore, your interest rate per month is, quick 0.015 or in easy terms 1.5 percent per month.
Credit cards that are paid in full each month attract little or no interest depending upon the terms and conditions of the merchant card offering.
But what happens if we only pay the minimum balance each month?
First month, your credit card principal balance is $2,000 times .015 (1.5%) interest rate charged = $30. Add to balance = $2,030.
You make the minimum payment of $25 per month. $2,030 minus $25 = $2,005 remaining balance.
Second month, interest charged on $2,005 times 1.5% = $30.08. Add the interest to the balance $2,035.08.
Subtract your minimum payment of $25 = remaining balance of $2,010.08
Third month ?- calculate the interest on $2,010.08 times 1.5% = $30.15 and add to the balance = $2,040.23
This balance will continue to escalate unless more than the minimum payment is applied. What did you absolutely have to have that you are still paying for months later?
Now think about how hard you have to work to save any money at a much lower interest rate. Financial literacy, it is up to you. Need I say more?
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While I abhor the term ?dummy?, an excellent book for those wanting to hone their everyday math skills is ?Everyday Math for Dummies.? The author, Charles Seiter, Ph.D. wrote his first math book at the age of ten, a cartoon guide to calculus that was used as part of a junior college maths course.
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Martha Harris Myron CPA/PFS CFP? is a dual citizen (Bermudian/US). She specialises in planning and investment advisory services for clients considering lifestyle transitions and rewarding retirements. Confidential email can be directed to marthamyronnorthrock.bm or 294-5709
The article expresses the opinion of the author alone. Under no circumstances is the content of this article to be taken as specific investment or financial planning advice, nor as a recommendation to buy/ sell any investment product.