Talking Cash: Napkin math
Financial math is usually complicated,
but not always. Here are a
few quick formulas that you can do
on your computer, on the back of a
napkin or even just in your head.
They'll help with things like figuring
out what return on an investment
you're getting, how long something
should be invested and a neat little
tip for quickly figuring out a job's
annual salary based on its hourly
wage.
Have you heard of the Rule of 72? It's a quick formula for figuring out the approximate numbers of years your investment will double based on its interest rate. I have no idea why the formula uses the number 72 specifically, but some math whiz figured this one out a long time ago. So, for example, if you wanted to know how long it will take to double your money at five per cent interest, divide 72 by five and you get approximately 14.4 years.
The rule of 72 is great for understanding the effect of compound interest on investments. As another example, if you divide 72 by seven, you get 10.3 years. So, comparing these two examples, the investment with the five per cent interest rate will double in 14.4 years, whereas the investment with the seven per cent interest rate will double in 10.3 years. I suppose it's obvious that a seven per cent investment is going to have a better return than a five per cent investment, but the Rule of 72 gives you an idea of how long it will take for your investment to double.
The Rule of 72 also works for interest on debt. It gets kinda scary here. Consider a credit card that charges 20 per cent interest, which is pretty typical for most standard cards issued by the big banks. Divide 72 by 20 and you get 3.6. All it will take for your credit card balance to double, no matter how high or low the balance is, is 3.6 years if your card is charging you 20 per cent. For example, if you have $5,000 on your card now, in 3.6 years it will be $10,000. Another 3.6 years later, just over seven years in total, it will be $20,000. In over 10 years it will be $40,000. In 10 years, your credit card debt could actually go from $5,000 to $40,000 without making a single additional purchase on the card, as the interest rate alone causes the debt to skyrocket. Frightening.
A somewhat less scary form of financial napkin math is the salary trick. I use this one all the time. It's handy in job interviews or applications if you're trying to figure out how much approximate annual salary a position pays if the only info you have is the hourly wage, or vice versa. So, if a full-time position pays $15 an hour and you want to figure out how much that would be working full-time hours in a year, you double the 15 to 30 and then add three zeros to make $30,000. Thus, your approximate annual salary of $15 per hour is $30,000. Using another example, if you're earning minimum wage at $10.25, double that to 20.5 and add two zeros (because of the five after the decimal point) to get $20,500.
You can also do this in reverse. If you are offered a job that pays an hourly wage, but you only know the annual salary of $40,000, all you have to do is take away the three zeros on the end to make it 40, and then divide in half, which gives you $20 per hour. This trick doesn't factor in things like taxes, CPP, EI payments or anything else that would drastically change the formula. It's inexact, but it's meant to give you a quick idea of salary expectations so that if you are in a job interview and the interviewer mentions the position pays $15, you can quickly approximate that to $30,000 per year.
Jeremy Wall is studying Professional Financial Services at Fanshawe College. He holds an Honours Bachelor of Arts from the University of Western Ontario.
Have you heard of the Rule of 72? It's a quick formula for figuring out the approximate numbers of years your investment will double based on its interest rate. I have no idea why the formula uses the number 72 specifically, but some math whiz figured this one out a long time ago. So, for example, if you wanted to know how long it will take to double your money at five per cent interest, divide 72 by five and you get approximately 14.4 years.
The rule of 72 is great for understanding the effect of compound interest on investments. As another example, if you divide 72 by seven, you get 10.3 years. So, comparing these two examples, the investment with the five per cent interest rate will double in 14.4 years, whereas the investment with the seven per cent interest rate will double in 10.3 years. I suppose it's obvious that a seven per cent investment is going to have a better return than a five per cent investment, but the Rule of 72 gives you an idea of how long it will take for your investment to double.
The Rule of 72 also works for interest on debt. It gets kinda scary here. Consider a credit card that charges 20 per cent interest, which is pretty typical for most standard cards issued by the big banks. Divide 72 by 20 and you get 3.6. All it will take for your credit card balance to double, no matter how high or low the balance is, is 3.6 years if your card is charging you 20 per cent. For example, if you have $5,000 on your card now, in 3.6 years it will be $10,000. Another 3.6 years later, just over seven years in total, it will be $20,000. In over 10 years it will be $40,000. In 10 years, your credit card debt could actually go from $5,000 to $40,000 without making a single additional purchase on the card, as the interest rate alone causes the debt to skyrocket. Frightening.
A somewhat less scary form of financial napkin math is the salary trick. I use this one all the time. It's handy in job interviews or applications if you're trying to figure out how much approximate annual salary a position pays if the only info you have is the hourly wage, or vice versa. So, if a full-time position pays $15 an hour and you want to figure out how much that would be working full-time hours in a year, you double the 15 to 30 and then add three zeros to make $30,000. Thus, your approximate annual salary of $15 per hour is $30,000. Using another example, if you're earning minimum wage at $10.25, double that to 20.5 and add two zeros (because of the five after the decimal point) to get $20,500.
You can also do this in reverse. If you are offered a job that pays an hourly wage, but you only know the annual salary of $40,000, all you have to do is take away the three zeros on the end to make it 40, and then divide in half, which gives you $20 per hour. This trick doesn't factor in things like taxes, CPP, EI payments or anything else that would drastically change the formula. It's inexact, but it's meant to give you a quick idea of salary expectations so that if you are in a job interview and the interviewer mentions the position pays $15, you can quickly approximate that to $30,000 per year.
Jeremy Wall is studying Professional Financial Services at Fanshawe College. He holds an Honours Bachelor of Arts from the University of Western Ontario.
