Learn The Math - Part 3

Saving Money Tip #199 – Learn The Math – Part 3. In parts 1 and 2 of this series, I discussed why it is important to learn some basic math concepts in order to help you save money. In part 1 we talked about calculating percentages, and in part 2 we discussed figuring out fractions. Today, we are going to talk about figuring out compounding interest rates on investments. Interest rates are calculated by multiplying the percentage by the original number. Compounding simply means that you get interest on the interest.

Suppose you are looking at investing some money – let’s say $1,000 – for the relative short term of 1 to 3 years. You look at some banks to compare interest rates. The bank says they will pay an annual interest rate of 1% if you put your $1000 into a savings account. For the sake of simplicity, let’s assume the interest is compounded annually. And then you find an online bank that is running some special rates to get you to become a customer. Their savings account will pay a 2% annual rate. How much will you get if you keep your money there for three years?

Well, we already discussed in Part 1 of this series how to figure out the percentages, so let’s use that knowledge. One percent of $1,000 is $10. That means if you invest $1,000 for one year, you will have $1,010 at the end of year one. If you keep the money in there for a second year, you will have $1020.10. That is because you now have $1010 earning 1% interest. One percent of $1010 is $10.10. Add $10.10 to the $1010 that you had at the end of year one and you will now have $1020.10. If you keep the money in the bank for a third year, you will have $1030.30 ($1020.10 x 1% is $10.20. Add $10.20 to the $1020.10 that you had at the end of year two to get $1030.30). By keeping the money in the bank for three years and earning 1% interest per year, your $1000 has grown to $1030.30.

Now, let’s look at the online bank. They are promising you a rate of 2% annually. Let’s figure out your interest. At the end of year one, you will have $1020 (1000 x 2% = $20 in interest + the original $1000). At the end of year two you will have $1040.40 ($1020 x 2% = $20.40 + $1020 that you had at the end of year 1). At the end of year three you will have $1061.21. (1040.40 x 2%=$20.81 + the $1040.40 you had at the end of year 2). So now you were able to calculate the interest and the final amount you will receive after three years. Keep in mind that many banks compound interest more often than annually (maybe daily or monthly) so the final amount may be a bit higher, but this should get you close enough comparison.

Let’s compare. If you put your money in a savings account for three years earning 1% interest compounded annually then you will have $1030.30 at the end of year 3. Or if you put it in a bank account earning 2% interest compounded annually, you will have $1061.21 at the end of three years. Now of course, this assumes that rates don’t change at either bank during the course of three years. But regardless this example shows how to calculate interest rates.

Everyone should be able to figure out the approximate interest rates that a bank savings account or CD is paying. You can use a calculator to do the calculations, but it is a good idea to understand how to compute the numbers manually.

In Real Life (IRL) – When I was younger I used to set up spreadsheets on the computer figuring out how much my money would be worth at some future date if it was earning x% each year. It was neat to see how the compounding made my money grow so much faster. By inputting the amount of money I was putting into an account and estimating the percent interest I was getting, I would get excited by how much money I would have at a far off date in the future. This served as a motivating factor for me to keep saving my money. By changing the interest rates, I could see the difference in the amount my money would be worth if I earned a higher percentage or lower percentage.

This sometimes led me to look for CDs that paid higher interest rates or savings accounts that offered more competitive rates. Of course, with the CDs, the rates were guaranteed for a set period of time, whereas the savings account rates could change at any time, but it still gave me an idea of how striving to find higher returns on my money could make my money grow faster.

There are many online programs and calculators that can do the same thing for you. And they are good motivators to keep up your savings pace and earn the best interest rate that you can. If you don’t have a computer near by or a calculator handy, then you can calculate the interest rates with paper and pencil using the method above to figure out the approximate amount of money you will make at a certain interest rate. Don’t get scared by the numbers or the percentages. The nice thing about being able to figure out the math is that there is only one correct answer. And if you practice enough with it, you will have a good understanding of how interest rates work and see how higher ones will work faster to grow your money.