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 Welcome to the Teachers' Choice Software web site. Our FREE on line mathematics 'How-To' library is open 24 hours a day.  The ever-growing library now has 71 helpful topics, and every topic includes a free download! For the 'How-to' library topic on simple interest, click here.

This topic is part of the Algematics help database, and shows you how you can use Algematics to solve simple interest problems.

### Theory:

When you borrow money, if the repayment amount is calculated based on simple interest (also known as flat rate interest), interest is charged each year on the full amount borrowed at the beginning.

To calculate the total interest, ' I ', that you will pay on a simple interest loan, you use this formula:

I = PRT

where:

'P' is the 'principal', the amount borrowed.
'
R' is the 'rate' percent of interest per year. The rate is calculated by dividing the yearly interest percentage by 100. For example, if 12.5% interest is changed per year, then R = 12.5 ¸ 100, = 0.125
'
T' is the number of years that you will be paying back the loan.

You have to pay back both the principal that you borrowed, as well as the interest. If you make monthly payments, you can easily calculate the payment amount. Just add the total interest to the principal, then divide this by the number of months that you will be paying the loan back.

### Method:

Consider these simple interest problems:

Example 1
To buy a computer, Tom borrowed \$3000 at 9% simple interest calculated yearly. If he will be making monthly payments for four years, calculate:

(a) the amount of interest to be paid,
(b) the total amount to be paid back,
(c) the monthly payment amount.

Example 2
When Jane bought her V.C.R., she borrowed \$500 at 5% simple interest. The total interest payable over the period of the loan is \$50. How many years will it take her to repay the loan?

To do both of these problems, you enter the simple interest formula: I = PRT, substitute for the known quantities, simplify to a final answer, then answer the specific questions. These steps are explained below.

Step 1  Enter the simple interest formula
Click and type the simple interest formula into the maths box in the data entry dialog box.

If the 'EMPTY' message is not displayed between the blue buttons, click the button until the message: 'INSERT' appears.

Maths...

I = PRT

and then click

Step 2  Substitute for the known quantities

Click on the input box, then enter the known values, like this:

Example 1:

P = 3000, R = 9.0/100, T = 4

Example 2:

I = 50, P = 500, R = 5.0/100

Now click the (substitute) button.

NOTE: Include a decimal point in the interest value, even if it is a whole number. This forces the calculations to display as decimals instead of fractions.

Step 3  Simplify to a final answer

Click the (simplify) button several times until a solution to the simple interest equation is found. These are the results for the two examples:

Example 1:

I = 1080

Example 2:

50 = 25T

In this case, you must divide both sides of the equation by 25 to find T. To do this with Algematics, click on the input box and type 25. Now click the button and then the (simplify) button. This will reduce this equation to:

2 = T

Now that the unknown quantities have been calculated, the questions in examples 1 and 2 above can be answered.

Example 1:

(a) The amount of interest to be paid back is \$1080
(b) The total amount to be paid back is \$3000 + \$1080 = \$4080
(c) The monthly payment amount = (total to be repaid) ¸  (number of months)

= \$4080 ¸ 48

= \$85

Example 2:

Jane will take 2 years to repay her loan.

### Practice:

Use Algematics to solve these simple interest problems:

(1) Ernie borrowed \$5500 for a new motor bike, to be paid back over 5 years. The bank is charging him 12% simple interest, calculated yearly. Calculate:

(a) the total interest that will be paid back,
(b) the total to be paid back,
(c) the monthly payment amount.

(2) Linda borrowed \$1500 at 5% simple interest per year, for an overseas holiday. Over the period of the loan she will pay \$250 in interest. How long will Linda be making monthly payments?