# Simple Interest Formulas, Shortcuts and Study Material

Interest is the cost of borrowing money.An interest rate is the cost stated as a percent of the amount borrowed per period of time, usually one year.

Simple Interest: Simple interest is calculated on the original principal only.Accumulated interest from prior periods is not used in calculations for the following periods. Simple interest is normally used for a single period of less than a year, such as 30 or 60 days.
Simple interest =$(\frac{P\times R\times T}{100})$

P = principal (original amount borrowed or loaned)
R = interest rate for one period
T = number of periods

Principal: The money borrowed or lent out for a certain period is called the principal or the sum.

Interest: Extra money paid for using other's money is called interest.

Simple Interest (S.I.): If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then

(i) Simple interest=$(\frac{P\times R\times T}{100 })$

(ii) P=$\left [ \frac{100\times S.I}{R\times T} \right ] ;R=\left [ \frac{100\times S.I}{T\times R} \right ] and\, T=\left [ \frac{100\times S.I}{P\times R} \right ]$

## Simple Interest Formulas

Example 1. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

Explanation:
S.I. for 1 year = Rs. (854-815) = Rs. 39.
S.I. for 3 years = Rs.$(39\times 3)$ = Rs. 117.
Principal = Rs. (815-117) = Rs. 698.

Example 2.Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?

Explanation:
Let the sum invested in Scheme A be Rs.x and that in Scheme B be Rs. (13900-x).
Then,$\left ( \frac{x\times 14\times 2}{100} \right )+\left ( \frac{(13900-X)\times 11\times 2}{100} \right )$=3508.
$\Rightarrow 28x-22x=350800 -(13900\times 22)$
$\Rightarrow 6x=45000$
$\Rightarrow x=7500$
So, sum invested in Scheme B = Rs. (13900-7500) = Rs. 6400.

Example 3. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years.What is the sum?

Explanation:
Principal= Rs.$\left [ \frac{100\times 4016.25}{9\times 5} \right ]$
= Rs.$\left [ \frac{401625}{45} \right ]$ = Rs. 8925

Example 4. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Explanation:
Time =$\left [ \frac{100\times 81}{450\times 4.5} \right ]$ years = 4 years.

Example 5. A person takes a loan of Rs. 200 at 5% simple interest. He returns Rs. 100 at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay:

Explanation:
Amount to be paid
= Rs.$\left ( 100+\frac{200\times 5\times 1}{100}+\frac{100\times 5\times 1}{100} \right )$ = Rs.115.

## Simple Interest Questions from Previous Year Exams

IBPS questions related to Simple and Compound Interests

## Simple Interest Video Lecture

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