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...**

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
= 25*T*

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*

**Step
4** Answer the questions

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.

**Return
to step 1 above to do more simple interest problems. **

### 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?

### [
Answers provided in Algematics help file.]