# Simple Interest

Pratice Simple Interest Questions and answers.

## Importance of Simple Interest

A lot of questions on simple interest are asked in different competitive exams. You are required to have mastery on the concept of Simple Interest in order to solve Compound Interest questions.

## Simple Interest - Scope of Questions

Simple interest questions don’t have much variation. Here are the questions you need to find out: Principal, interest, rate, time or amount. Questions on two interest rates for different times may also be asked.

## Simple Interest - Way to Success

All questions are based on a single basic formulae, but to increase speed, direct formulae are required too.

## Simple Interest - Important Points

1. Principal: Borrowed money is called Principal and it is denotedby ‘P’.
2. Interest Time: Money is borrowed for certain time period, that time is called interest time and it is denoted by ‘T’ or ‘t’.
3. Amount: The principal becomes Amount when interest is added to it. Amount is represented as A.
• Amount = Principal + Interest

$A = P + SI$

• Interest = Amount – Principal

$SI = A – P$

4. When Interest is payable half-yearly:
• Rate will be half
• time will be twice
5. When Interest is payable quarterly:
• Rate will be one-fourth
• time will be four times

## Simple Interest - Basic Rules

Rule Description
1

Simple interest = $\frac{Principal \times Time \times Rate}{100}$

i.e.

$S.I. = \frac{P \times R \times T}{100}$

2

Principal (P) = $\frac{100 \times S.I.}{R \times T}$

3

Rate (R) = $\frac{100 \times S.I.}{T \times P}$

4

Time (T) = $\frac{100 \times S.I.}{P \times R}$

5

If rate of Simple Interest differs from year to year, then

$S.I. = P \times \frac{\left(R_1 + R_2 + R_3 + .....\right)}{100}$

6

Amount = Principal + Interest

i.e.

• $A=P+I$
• $A=P+\frac{PRT}{100}$
• $A=P\left(1+\frac{RT}{100}\right)$
7

If $\frac{1}{x}$ part of a certain sum P is lent out at R1 % SI, $\frac{1}{y}$ part is lent out at R2 % SI and the remaining $\frac{1}{x}$ part at R3 % SI and this way the interest received by 1, then

$P=\frac{1\times100}{\frac{R_1}{x}+\frac{R_2}{y}+\frac{R_3}{z}}$

8

If a sum of money becomes n times in T years at simple interest, then formula for calculating rate of interest will be given as

$R=\frac{100\left(n-1\right)}{T}\%$

9

If a sum of money at a certain rate of interest becomes n times in T1 years and m times in T2 years, then formula for T2 will be given as

$T_2=\frac{\left(m-1\right)}{\left(n-1\right)}\times T_1$

## Simple Interest - Important Rules & Shortcut Tricks

Rule Description
1

Simple Interest = $\frac{Principal \ \times \ Rate \ \times \ Time}{100}$

• SI = $\frac{P\times R\times T}{100}$
• P = $\frac{SI\times 100}{R \times T}$
• R = $\frac{SI\times 100}{P \times T}$
• T = $\frac{SI\times 100}{P \times R}$
2
• A = $P+SI$
• SI = $A-P$
• P = $A-SI$
3

If there are distinct rates of interest for distinct time periods i.e.

• Rate for 1st t1 years = R1%
• Rate for 2nd t2 years = R2%
• Rate for 3rd t3 years = R3%

Then, Total S.I. for 3 years =

$\frac{P\left(R_1t_1+R_2t_2+R_3t_3\right)}{100}$

4

If a certain sum becomes ‘n’ times of itself in T years on Simple Interest, then the rate percent per annum is.

• $R\% = \frac{\left(n-1\right)}{T}\times100\%$
• $T\% = \frac{\left(n-1\right)}{R}\times100\%$
5

If a certain sum becomes n1 times of itself at R1% rate and n2 times of itself at R2% rate, then,

• $R_2=\frac{\left(n_2-1\right)}{\left(n_1-1\right)}R_1$
• $T_2=\frac{\left(n_2-1\right)}{\left(n_1-1\right)}T_1$
6

If Simple Interest (S.I.) becomes ‘n’ times of principal (P) i.e.

$S.I. = P × n$, then

• $RT=n\times100$
• $R = \frac{n × 100}{T}$
• $T = \frac{n × 100}{R}$
7

If an Amount (A) becomes ‘n’ times of principal (P) i.e.

$A = Pn$, then

• $RT = (n – 1) × 100$
• $R=\frac{(n-1)\times100}{T}$
• $T=\frac{(n-1)\times100}{R}$
8

If the difference between two simple interests is ‘x’ calculated at different annual rates and times, then principal (P) is

$\frac{x\times100}{(difference\ in\ rate)\times(difference\ in\ time)}$

9

If a sum with simple interest rate, amounts to ‘A’ in t1 years and ‘B’ in same t2 years, then

• R% = $\frac{\left(B-A\right)\times100}{A.t_2-B.t_1}$
• P = $\frac{At_2-Bt_1}{t_2-t_1}$
10

If a sum is to be deposited in equal installments, then,

Equal installment =

$\frac{A\times200}{T\left[200+\left(T-1\right)r\right]}$

where

• T = no. of years
• A = amount
• r = Rate of Interest
11

To find the rate of interest under current deposit plan,

$r=\frac{SI\times2400}{n\left(n+1\right)\times\left(deposited \ amount\right)}$

where, n = no. of months.

12

If certain sum P amounts to Rs. A1 in t1 years at rate of R% and the same sum amounts to Rs. A2 in t2 years at same rate of interest R%. Then,

• $R=\left(\frac{A_1-A_2}{A_2T_1-A_1T_2}\right)\times100$
• $P=\left(\frac{A_2T_1-A_1T_2}{T_1-T_2}\right)$
13

The difference between the S.I. for a certain sum P1 deposited for time T1 at R1 rate of interest and another sum P2 deposited for time T2 at R2 rate of interest is

$SI=\frac{P_2R_2T_2-P_1R_1T_1}{100}$