Simple Interest
Simple Interest

Simple Interest (SI) with Short Tricks

Simple Interest (SI) with Short Tricks

for all competitive exams i.e., IAS/PCS/SSC/Bank/Railway/NTPC/SI etc

Simple interest is an easy method of calculating interest charges based on the original sum/ principal amount of a deposit or a loan

Following terms are related to interest

  1. Principal /Sum (P) – Principal is the money that borrowed or deposited for certain time.
  2. Rate of interest (R) – Interest charged on principal or sum.
  3. Time (T) – The period for which money is borrowed or deposited
  4. Amount (A) – Sum of Principal and Interests, that is P+A

Some Basic Formula of Simple Interest (SI) and others;

SI\ =\ \frac{P\times\R\times T}{100}\\

P\ =\ \frac{SI\times100}{R\times T}\\

R\ =\ \frac{SI\times100}{P\times T}\\

T\ =\ \frac{SI\times100}{P\times R}\\

A = P + SI

Some Hints or Tricks if Interest charged by Monthly/Quarterly/Half Yearly

  1. If rate of interest charged Half Yearly then.
New\ Rate\ R =\frac{R}{2}\% 

and New Time T = 2T

2. If rate of interest charged Quarterly then.

New\ Rate\ R =\frac{R}{4}\%

and New Time T = 4T

3. If rate of interest charged Monthly then.

New\ Rate\ R =\frac{R}{12}\%

and New Time T = 12T

4. If rate of interest charged Yearly/Annually then.

 New Rate R = R% and New Time T = 12T

Some Example based on basic concept of SI

Example1. Find the simple interest and Amount on the sum of Rs. 5000 at the rate of 5% for 2 years.

Here, P = 5000, R = 5% and T = 2 Yr. are given

Hence

SI\ =\ \frac{P\times\R\times T}{100}\ =\ \frac{5000\times5\times2\ }{100}\ =\ 500

And Amount A= P+SI = 5000+500 = 5500

Example2. Find the simple interest and Amount on the sum of Rs. 5000 at the rate of 6% half yearly for 2 years.

Here, P = 5000, R = 6% and T = 2 Yr. are given

Now the rate of interest is half yearly

Therefore, New Rate of Interest R = R/2 = 6/2 = 3%

And New Time T = 2T = 22 = 4 yr Hence

SI\ =\ \frac{P\times\R\times T}{100}\ =\ \frac{5000\times3\times4\ }{100}\ =\ 600

And Amount A= P+SI = 5000+600 = 5600

Example3.

Mohit pays Rs 9000 as an amount on the sum of Rs 7000 that he had borrowed for 2 years. Find the rate of interest.

SI = (P × R ×T) / 100 

R = (SI × 100) / (P× T)

R = (2000 × 100 /7000 × 2) =14.29 % 

Thus, R = 14.29%

Short Tricks for Competitive Exams

T1. If a sum of money becomes n times in T yr at simple interest, then rate of interest will be

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

Example 4.  A sum of money becomes 4 times in 20 yr at Simple Interest. Find the rate of interest.

Here n = 4 and T = 20yr Therefore,

R=\ \frac{100(4-1)}{20}\%
=\ 5\times3\% =15\%
That means if the rate of interest is 15% then the sum of money becomes 4 times in 20 years.

T2. If a sum of money at a certain rate of interest becomes n times in T1 yr and m times in T2 yr, then

T2 =\frac{(m-1)}{(n-1)}\times\mathbf{T1}

T3. If a sum of money in a certain time becomes n times at R1, rate of interest and m times at R2 rate of interest, then

R2=\frac{(m-1)}{(n-1)}\times\mathbf{R1}

Example. In a certain time, a sum becomes 3 times at the rate of 5% per annum. At what rate of interest, the same sum becomes 6 times in same duration?

Here, m = 6, n= 3 and R1 = 5%

R=\frac{(6-1)}{(3-1)}\times\mathbf{5}\ =\ \frac{\mathbf{5}}{\mathbf{2}}\times\mathbf{5}\% =\ \mathbf{25}/\mathbf{2}\% =\ \mathbf{12}.\mathbf{5}\%\ 

T4. If a certain sum P in a certain time amounts to A1, at the rate of R1% and the same sum amounts to A2at the rate of R2%, then

P=\ \frac{A_2R_1-A_1R_2}{R_1-R_2}\ and\ T\ =\ \frac{A_1-A_2}{A_2R_1-A_1R_2}\ \times100

T5. If a certain sum P in a certain rate of interest amounts to A1, in T1 year and the same sum amounts to A2in T2 year then

P=\ \frac{A_2T_1-A_1T_2}{T_1-T_2}\ and\ R=\ \frac{A_1-A_2}{A_2T_1-A_1T_2}\ \times100

Example. A certain sum in certain time becomes 500 at the rate of 8% per annum SI and the same sum amounts to 200 at the rate of 2% per annum SI in the same duration. Find the sum and time.

P = 200 ×8 – 500×2 / 8-2 = 1600-1000/6 = 600/6 = Rs. 100

T= (500-200/200 ×8 – 500×2) ×100 = 300/600 ×100 = 50yr

Example. A certain sum at a certain rate of SI amounts to Rs. 1125 in 4 yr and Rs. 1200 in 7 yr. Find the sum and rate of interest.

P = 1200 ×4 – 1125×7 / 4-7 = 4800-7875/-3 = -3075/-3 = Rs. 1025

R= (1125-1200/1200 ×4 – 1125×7) ×100 = -7500/-3075 = 2.43%

T6. A sum of P is lent out in n parts in such a way that the interest on first part at R1 % for T1 yr, the interest on second part at R2 % for T2 yr and the interest on third part at R3 % for T3 yr and  so on, are equal, then the ratio in which the sum was divided in n parts is given by

\frac{1}{R_1T_1}\times\frac{1}{R_2T_2}\times\frac{1}{R_3T_3}\times\ .\ \ .\ \ .\ \ .\ \ \times\frac{1}{R_nT_n}

T6. The annual payment that will discharge a debt of Rs. P due in Tyr at the rate of interest R% per annum is given by

Annual\ payment\ =\ \ \frac{100P}{100T+\frac{RT(T-1)}{2}}

Example. What annual payment will discharge a debt of Rs. 848 in 8 yr at 8% per annum?

Here P = 848, R = 8% and Time T = 8 yr

Annual\ payment\ =\ \ \frac{100\times848}{100\times8+\frac{8\times8(8-1)}{2}}
=\ \frac{84800}{800+32\times7}\ =\ \frac{84800}{1024}\ \ =\ 82.8125

T7. If 1/x part of a certain sum P is lent out at R1 % SI, 1/y part is lent out R2 % SI and the remaining 1/z part at R3 % SI and this way the interest received be I, then principal amount P

{P}\ =\ \ \frac{I\times100}{\frac{R1}{x}+\frac{R2}{y}+\frac{R3}{z}}

Example. Ram lent out a certain sum. He lent 1/3 part of his sum at 7% SI, 1/4 part at 8% SI and remaining part at 10% SI. If Rs. 510 is his total interest, then find the money lent out.

Here, 1/x = 1/3, 1/y = ¼ and the remaining part

1/z = 1- (1/3 + ¼) = 1 – 7/12 = 12-7/12 = 5/12

And R1 = 7%, R2 = 8% , R3 = 10% and Interest I = 510

Now

{P}\ =\ \ \frac{I\times100}{\frac{R1}{x}+\frac{R2}{y}+\frac{R3}{z}}
{P}\ =\ \ \frac{510\times100}{\frac{7}{3}+\frac{8}{4}+\frac{50}{12}}
{P}\ =\ \ \frac{51000}{51}\times6\ =\ 6000

T8. If SI for a certain sum P1, for time T1 and rate of interest R1, is I1, and SI for another sum P2 for time T2 and rate of interest R2is I2, then Difference

\ SI\ =\ I_{2\ }-\ I_1=\ \frac{P_2R_2T_2-P_1R_1T_1}{100}

In this regard we found four cases as follows;

  1. In the above-mentioned condition, if all the parameters are constraint but time is variable, then
I_{2\ }-\ I_1=\ \frac{PR(T_2-T_1)}{100}

2. If only rate of interest is variable then

I_{2\ }-\ I_1=\ \frac{PT(R_2-R_1)}{100}

3. If only sum is variable then

I_{2\ }-\ I_1=\ \frac{{RT(P}_2-P_1)}{100}

4. If only one parameter remains constant and the remaining are variables then

	I_{2\ }-\ I_1=\ \frac{{P(R}_2T_2-R_1T_1)}{100}
	I_{2\ }-\ I_1=\ \frac{{R(P}_2T_2-P_1T_1)}{100}
	I_{2\ }-\ I_1=\ \frac{{T(P}_2R_2-P_1R_1)}{100}

Example. Simple interest for the sum of Rs. 1500 is Rs. 50 in 4 yr and Rs. 80 in 8 yr. Find the rate of SI

Here, I1 = 50, I2 = 80, T1 = 4yr, T2 = 8yr, P = Rs. 1500

And principal and rate of interest are constants so,

I_{2\ }-\ I_1=\ \frac{PR\left(T_2-T_1\right)}{100}\ 
80-50=\ \frac{1500\times R\left(8-4\right)}{100}
30=\ 15\times R\times4

1 = 2R,

R = 0.5 %

Some Problems for Practices

  1. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% per annum in 5 years. What is the sum? 
  2. A sum of Rs. 725 is lent at the beginning of a year at a specific rate of interest. After eight months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both loans. What was the actual rate of interest?
  3. Simple interest on a certain sum is 16/25 of the sum. Find the rate of interest and time if both are numerically equal.
  4. A private finance company A claims to be lending money at simple interest. But the company includes the interest every 6 months for calculating principal. If company A is charging an in- terest of 10%, the effective rate of interest after 1 yr becomes

(a) 10.25% (b) 12.50% (c) 11.25% (d) 10.75%

5. The rates of simple interest in two banks x and y are in the ratio of 10:8. Rajni wants to deposit his total savings in two banks in such a way that she receive equal half-yearly interest from both. She should deposit the savings in banks x and y in the ratio of

(a) 4:5 (b) 3:5 (c) 5:4 (d) 2:1

6. Rakesh lent out X 8750 at 7% annual interest. Find the simple interest in 3yr.

(a) X 1870 (b) X 1837.50 (c) X 1560 (d) X 2200

7. Find the difference in amount and principal for X 4000 at the rate of 5% annual interest in 4 yr. [GIC 2007]

        (a) X 865.50 (b) X 865 (C) X 400 (d) X 800

8. At simple interest, a sum becomes 3 times in 20 yr. Find the time, in which the sum will be double at the same rate of interest. [RRB 2007]

(a) 8 yr (b) 10 yr (c) 12 yr (d) 14 yr

9. A sum was invested for 4 yr at a certain rate of simple interest. If it had been invested at 2% more annual rate of interest, then X 56 more would have been obtained. What is the sum? [GIC 2007]

10. The simple interest on a certain sum of money for 2V4 yr at 12% per annum is X 20 less than the simple interest on the same sum for 3% yr at 10% per annum. Find the sum.

(a) X 800 (b) X 750 (c) X 625(d) X 400 (e) None of the above


Leave a Reply