How to Manually Calculate your Interest

Hi, and welcome to this overview of word problems that involve interest! In this video, we’re going to look at how interest accrues on money over time and how to solve word problems that deal with this process. Let’s get started!

Whether the money in question is a savings account balance or a credit card debt, the process is the same. Interest grows very rapidly, as the equation that is used to accrue interest is exponential in nature.

Let’s first review the steps and terminology that are involved in calculating a percentage increase with a simple example.

Suppose you have $100 in a savings account that returns an annual interest rate of 1.7%. This means that your bank promises to pay you 1.7% of your $100 balance at the end of the year. To determine that amount, you must:

First, convert the percentage to its decimal representation by moving the decimal point two places to the left,

Which gives us 1.7 or $1.70.

This amount, $1.70, is the interest that is earned and added to your $100, which means that your new balance at the end of the year is $101.70.

These two steps can be combined for a more efficient process. If we start with a balance of $100 and add the calculated interest, .017times 100, the expression will look like this:

We can now recognize a common factor of 100 in each of the two terms of the expression. Factoring out that initial balance, which is sometimes referred to as the principal balance, gives us 100 times 1 plus .017:

Combining the terms in the parentheses results in a factor of 1.017, which when multiplied by $100 results in the new savings account balance at the end of the year, $101.70.

Let’s practice a few more examples using the one-step process of adding interest to a given amount at the end of one year.

Calculate the interest that is earned on a bank account balance of $1,235 with an annual percentage rate of 2.1%. Round your answer to the nearest cent.

Remember, we first need to convert 2.1% to its decimal. Then multiply this interest rate by the initial balance of $1,235. This gives us an interest amount of $25.94 earned at the end of the year.

Now that we know the interest amount, what would the ending balance be of the bank account after one year?

Remember, the initial balance plus the interest earned equals the ending balance after one year. So, in this case: 1,235 plus 25.94 is equal to $1,260.94.

Let’s think a step further. What would the account balance be at the end of two years, assuming that there were no banking fees and that you did not make any additional deposits or withdrawals? If you’d like, pause the video and see if you can come up with the answer yourself.

To figure this out, all we have to do is take the balance at the end of year one, $1,260.94, and multiply it by a factor of 1.021. The ending balance at the end of the second year would, therefore, be equal to:

The concept of time is very important in this type of problem, because the interest is added to the account balance at the end of each year. If we break things down a bit, it becomes very easy to see the pattern of the factors as each year passes.

Year Initial Ending
End Balance x Factor Balance
1 $1,235 x 1.021 = $1,260.94
2 $1,235 x 1.021 x 1.021 = $1,287.41
3 $1,235 x 1.021 x 1.021 x 1.021 = $1,314.45

At the end of the first year, our initial balance grows by 2.1%. At the end of year two, the annual percentage rate is compounded again on a larger value, and then again at the end of year three, and so on.

Now, what would your ending balance be at the end of year four?

Well, at the end of year four, the annual percentage rate, or APR, will have been compounded four times, which gives us a total of $1,342.05:

And that’s all there is to it! Now that we’ve gone through several problems together, you should be well on your way to mastering any interest-related word problem that’s thrown at you.

Thanks for watching, and happy studying!

Interest Word Problem Questions