GED Mathematical Reasoning: Understanding Simple Interest

  • Interest is a fee for using someone else’s money. When you invest money, the bank pays you a fee for allowing them to use your money. When you borrow money, you pay the lender a fee for the use of their money. In both cases, this fee is called: interest.
  • The amount of money invested or borrowed is called the principal. Simple interest is a special kind of interest based only on the amount invested or borrowed, an interest rate, the time frame (in years).
  • To calculate simple interest, we use the following formula:

I = p \times r \times t

I = interest
p = principal
r = rate (as a decimal)
t = time (in years)

 

Example 1

Robert invests $5,000 for 20 years at 3% interest. Using the simple interest formula, how much interest will he earn?

 

First let’s make a note of what it is we’re being asked to find. In this case, we’re being asked to find the amount of interest Robert will earn on his investment.  In terms of the formula, we need to find “I,” the interest.

Next, let’s identify the information we’re given. It’s a good idea to jot this down on your paper. We’re told that the amount of money invested is $5,000, the time frame is 20 years and the interest rate is 3%. When using the simple interest formula, remember to turn the percent into a decimal. To do so, move the decimal point two places to the left and drop the percent sign. You may need to add zeros as placeholders.

So we know p equals $5,000, t equals 20 and r equals 3%, which is 0.03 written as a decimal. Since we know the values for principal, time, and rate it makes sense that we would apply the simple interest formula to find the interest earned as the example directs us to do.

I = p \cdot r \cdot t \rightarrow I = \$5000 \cdot 0.03 \cdot 20 = 3000

So the interest Robert will earn investing $5,000 over 20 years at a 3% simple interest rate is $3,000

Does the answer make sense? Well, 3% of $5,000 is $150, which we can find by multiplying 0.03 by $5,000 since the word “of” implies multiplication. And $150 per year for 20 years results in a total amount of $3,000. So yes, our answer makes perfect sense!

3\%\: of\: \$5000 = 0.03 \times \$5000 = \$150

\$150\, per \,year\, for\, 20\, years = \$150 \times 20 = \$3000

 

Example 2

Dexter borrows $1500 from his grandfather for 6 months at 2.5% simple interest. What is the total amount Dexter will pay back when the loan is due?

 

In example one, money was being invested. In this example money is being borrowed, however, to calculate the simple interest involves the same process either way.

When we read example two, we are told that the interest on this loan is being paid according to the simple interest calculation, but notice what we’re being asked to find. It’s not the interest. We need to find the total amount of money Dexter will repay.

First, let’s make a note of the information we’re given. We’re told that the amount of money borrowed is $1500, the time frame is 6 months and the interest rate is 2.5%. So we know p equals $1,500 and r equals 2.5%, which – as a decimal – is 0.025.

Let’s talk for a moment about the time frame, t. In the simple interest formula, the time frame needs to be in terms of years. Here, the time frame is given in terms of months. So how do we convert 6 months to years? Since there are twelve months in one year, we will convert 6 months to years by writing:  6 over 12. 6 months can be written as: one-half years. So, t equals 0.5

The interest rate is given in the example as a simple interest rate and we know the values for principal, rate, and time, so it makes sense that we would apply the simple interest formula to find the interest that Dexter will pay as a fee for borrowing the money. However, we’re not being asked to find the amount of interest. We’re being asked to find the total amount Dexter will repay, which consists of the amount of money borrowed PLUS the interest, which is the fee he will pay for borrowing the money.

Therefore, we need to find the amount of interest first. And then add the interest to the loan amount, making this a two-step problem. That sum will equal the total amount of money Dexter will repay to his grandfather.

Okay! Let’s get started.

First, we’ll find the amount of interest by applying the simple interest formula.

I = \$1500 \cdot 0.025 \cdot 0.5 = \$18.75[/latex]

So the interest on the loan is: $18.75. But we’re not done yet because we haven’t answered the question.

We must finish by accomplishing step 2 of our plan to find the total amount of money Dexter will repay to his grandfather. Dexter will repay the original loan amount of $1,500 plus interest in the amount of $18.75.

Total Amount Repaid = Original Loan Amount + Interest

Total Amount Repaid = $1500 + $18.75 = $1518.75

So the total amount of money Dexter will repay his grandfather is: $1,518.75. What do you think? Does this answer make sense?

$1,500 is not a huge loan amount, the interest rate is relatively low, and the time frame of the loan is very short – not even one year! So it makes sense that the interest amount would not be a very large number. Therefore, yes – our answer makes sense.

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