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This topic is part of the TCS FREE high school mathematics 'How-to Library'. It shows you how to solve simple interest problems. (See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.

Theory:

When someone lends money to someone else, the borrower usually pays a fee to the lender. This fee is called 'interest'. 'Simple' interest, or 'flat rate' interest. The amount of simple interest paid each year is a fixed percentage of the amount borrowed or lent at the start.

The simple interest formula is as follows:

Interest = Principal × Rate  ×  Time

where:  

'Interest' is the total amount of interest paid,

'Principal' is the amount lent or borrowed,

'Rate' is the percentage of the principal charged as interest each year. The rate is expressed as a decimal fraction, so percentages must be divided by 100. For example, if the rate is 15%, then use 15/100 or 0.15 in the formula.

'Time' is the time in years of the loan.

The simple interest formula is often abbreviated in this form:

I = P R T

Three other variations of this formula are used to find P, R and T:

                    

Simple interest problems can involve lending or borrowing. In both cases the same formulas are used.

Whenever money is borrowed, the total amount to be paid back equals the principal borrowed plus the interest charge:

total repayments = ( principal + interest )

Usually the money is paid back in regular instalments, either monthly or weekly. To calculate the regular payment amount, you divide the total amount to be repaid by the number of months ( or weeks ) of the loan. Like this:

OR:

  

To convert the loan period, 'T', from years to months, you multiply it by 12, since there are 12 months in a year. Or, to convert 'T' to weeks, you multiply by 52, because there are 52 weeks in a year.

The example problem below shows you how to use these formulas:

Example:

A student purchases a computer by obtaining a simple interest loan. The computer costs $1500, and the interest rate on the loan is 12%. If the loan is to be paid back in weekly instalments over  2 years, calculate:

1. The amount of interest paid over the 2 years, 

2. the total amount to be paid back,

3. the weekly payment amount.

   Given: principal: 'P' = $1500, interest rate: 'R' = 12% = 0.12, repayment time: 'T' = 2 years

 

Part 1: Find the amount of interest paid.

interest: 'I' = PRT

                    = 1500 × 0.12 × 2

                    = $360

Part 2: Find the total amount to be paid back.

total repayments = principal + interest

                                   =  $1500 + $360

                                   =  $1860

Part 3: Calculate the weekly payment amount

 

                                                               total repayments

  weekly payment amount = ---------------------------------------

                                                          loan period, T, in weeks

 

                                                            $1860

                                                    = -------------------

                                                             2 × 52

 

                                          =  $17.88 per week

Method:

Maths Helper Plus can solve many kinds of simple interest problems. It will do calculations showing the working steps, as well as display a labelled diagram.  

Step 2  Display the parameters box

Press the F5 key to display the parameters box:

 

You enter the given information into these edit boxes as follows:

        edit box 'A' = I, the amount of interest ($)

        edit box 'B'  = P, the principal lent or borrowed ( $ )

        edit box 'C' = R, the interest rate (%)

        edit box 'D' = T, the period of the loan (years)

 

Set any three of A, B, C and D to the values you are given.

Set the unknown value to zero.

Out of the four edit boxes A, B, C and D, three will not be zero, and one will be zero.

 

NOTE: The parameters box diagram shows the correct settings for solving the example from the 'Theory' section above.

'A' = 0, because we are calculating the unknown interest amount.

'B' = 1500, this is the principal borrowed.

'C' = 12, because the interest rate, R = 12%.

'D' = 2, because the loan is for 2 years.

Click the 'Update' button to refresh the diagram and calculations.