maths > commercial-arithmetics

Simple Interest

what you'll learn...

overview

Simple interest is made easy with the following.

Maturity Value $A$$A$ = Principal $P+$$P +$ Interest $PRT$$P R T$
$=P\left(1+R+R+R...T$ times)
Note: R is the (interest rate in percentage)/100.

The interest is calculated on the principal for each of the time period in $T$$T$. That is, the interest $PR$$P R$ is added $T$$T$ times.

Once the above is understood, the equation is easily derived.

idea of loan

A person takes a loan:

The principal is $1,00,000$$1 , 00 , 000$ coins
interest rate is $10%$ per annum
loan duration (time) is $1$$1$ year

interest in one year = principal $×$$\times$ time $×$$\times$ interest rate $/100$$/ 100$
= $1,00,000×1×10/100$$1 , 00 , 000 \times 1 \times 10 / 100$
$=10,000$$= 10 , 000$coins

At the end of loan duration, the person returns maturity value
maturity value = principal $+$$+$ interest
$100000+10000=1,10,000$$100000 + 10000 = 1 , 10 , 000$coins

simple to calculate

A person takes a loan:

The principal is $1,00,000$$1 , 00 , 000$ coins.
Simple interest rate is $10%$ per annum
loan duration (time) is $3$$3$ years.

interest in one year = principal $×$$\times$ interest rate $×$$\times$ time $/100$$/ 100$
= $1,00,000×10×3/100$$1 , 00 , 000 \times 10 \times 3 / 100$
$=30,000$$= 30 , 000$coins

At the end of loan duration, the person returns maturity value
maturity value = principal $+$$+$ interest
$100000+30000=1,30,000$$100000 + 30000 = 1 , 30 , 000$

Note: This form of interest is called simple interest.

understand

The word "simple" means: plain and basic form; presented without any complexity.

Simple Interest : Interest charged for a loan duration only on the principal is simple interest.

Let us understand how interest rate is specified.

Interest rate is given as $10%$ per annum. This means the following:

$10%$ means for every $100$$100$ coins, the interest is $10$$10$ coins

"per annum" means interest is for every year.

reference list

Students may find it difficult to memorize all the formulas for simple interest. This is listed for reference, and explained later. No need to memorize any of them.

principal $P$$P$
Interest Rate $R$$R$
Number of time periods $T$$T$
Maturity value or amount $A$$A$

Simple interest $S=PRT/100$$S = P R T / 100$
Maturity value $A=P+PRT/100$$A = P + P R T / 100$
Rate of interest $R=\left(A-P\right)×100/\left(PT\right)$$R = \left(A - P\right) \times 100 / \left(P T\right)$
Time period $T=\left(A-P\right)×100/\left(PR\right)$$T = \left(A - P\right) \times 100 / \left(P R\right)$
Principal $P=A×100/\left(1+RT\right)$$P = A \times 100 / \left(1 + R T\right)$

no need of the list

One need not memorize any formulas. Quickly follow through the story to recall formulas on the fly.

•  Interest is calculated as percentage of the principal. So, $I=PR/100$$I = P R / 100$ for every time period

•  Interest is calculated for a number of time periods. So, $I=PRT/100$$I = P R T / 100$ for all the time periods

•  The borrower has to return principal and the interest, which is the maturity value.

Maturity Value $A$$A$ = Principal $P+$$P +$ Interest $PRT/100$$P R T / 100$

There are $4$$4$ variables (A, P, R, T) in this equation. In a problem, $3$$3$ of these $4$$4$ variables are given and this formula is a form of linear equation of one variable (algebra) to solve for the unknown variable.

example

The principal $3000$$3000$ coins is returned as $4080$$4080$ coins in $3$$3$ years. Finding the simple interest rate per annum :

Given that
Principal $=3000$$= 3000$ coins
Maturity Value $=4080$$= 4080$ coins
Loan duration $=3years$$= 3 y e a r s$

substituting the given values in the equation
$A=P+PRT/100$$A = P + P R T / 100$
$4080=3000+3000×R×3/100$$4080 = 3000 + 3000 \times R \times 3 / 100$
$1080=90R$$1080 = 90 R$
$R=12%$

summary

Simple interest
Maturity Value $A$$A$ = Principal $P+$$P +$ Interest $PRT$$P R T$
$=P\left(1+R+R+R...T$ times)
Note: R is the (interest rate in percentage)/100.

The interest is calculated on the principal for each of the time period in $T$$T$. That is, the interest $PR$$P R$ is added $T$$T$ times.

Once the above is understood, the equation is easily derived.

Maturity Value $A$$A$ = Principal $P+$$P +$ Interest $PRT/100$$P R T / 100$

Outline