# Useful Shortcuts and Tricks for Simple Interest & Compound Interest

Dear Readers, Here we have given the Useful Shortcuts and Tricks for Simple Interest & Compound Interest Problems for IBPS Exams. This is the most important topic that comes with all the competitive exams.  Candidates have to give importance to this topic to enhance the score level. So candidates who are preparing for the upcoming IBPS exams can make use of these Useful Shortcuts and Tricks for Simple Interest & Compound Interest.

## Formula:

1) SI = P x R x T/100

2) Principal = Simple Interest ×100/ R × T
3) Rate of Interest = Simple Interest ×100 / P × T
4) Time = Simple Interest ×100 / P × R

5) If the rate of Simple interest differs from year to year, then

Simple Interest = Principal × (R1+R2+ R3…..)/100

The four variables in the above formula are:
SI=Simple Interest P=Principal Amount (This the amount invested)T=Number of yearsR=Rate of interest (per year) in percentage
1). A sum of money is divided into n parts in such a way that the interest on the first part at r1% for t1 years, on the second part at r2% for t2 years, on the third part at r3% for t3years, and so on, are equal. Then the ratio in which the sum is divided in n part is:
1/r1×t1: 1/r2 ×t2: 1/r3×t3
Example:
A sum of Rs 7700 is lent out in two parts in such a way that the interest on one part at 20% for 5 yr is equal to that on another part at 9% for 6 yr. Find the two sums.
Solution:
Here, R1 = 20% R2 = 9%

T1 = 5 yr T2 = 6 yr

By using formula, ratio of two sums  = 1/100 : 1/54 = 27 : 50

Therefore, first part = [27/(27+50)]*7700 = Rs 2700

Second part = [50/(27+50)]*7700 = Rs 5000

2). Amount = Principal + S.I = p + [(p x r x t)/100]
Example:
What Principal will amount to Rs. 16000 in 6 years at 10% simple interest?
Solution:

Let the principal be Rs. p, given rate of interest is 10% and time = 6 years.
Amount received at the end of 6 years = 16000 Rs.
=> 16000 = p + (p x 10 x 6)/100 = p + 6p/10 = 16p/10 => P = 16000 x (10/16) = 1000 x 10 = 10000 Rs.
The principal should be Rs. 10000

3). If sum becomes n times in T yr at simple interest, then the formula for calculating the rate of interest

R =100(n-1) /T %

4). A sum of money becomes 4 times in 20 yr at SI. Find the rate of interest?

R =100(4-1)/20
=100*3 / 20 =5*3 =15

5). If A sum becomes n times in a certain rate of interest .then the time taken in which the same amount will be n times at the same rate of interest:
= (n-1)/2 × T (n = number of times)

6). If A sum becomes 3 times in a certain rate of interest in 5years .find the time taken in  the same amount will be 8 times at the same rate of interest:
=(8-1)/2*5
= 7/2 * 5
=17.5years

## Useful Shortcuts and Tricks for Simple Interest & Compound Interest

### Compound Interest

The difference between the amount and the money borrowed is called the compound interest for a given period of time
1) Let principal =P; time =n years; and rate = r% per annum and let A be the total amount at the end of n years, then

A = P*[1+ (r/100)]n;
CI = {P*[1+ (r/100)]n -1}
2) When compound interest reckoned half-yearly, then r% become r/2% and time n becomes 2n;

A= P*[1+ (r/2*100)]2n
3) For the quarterly

A= P*[1+ (r/4*100)]4n
4) The difference between compound interest and simple interest over two years is given by

Pr2/1002or P(r/100)2
5) The difference between compound interest and simple interest over three years is given by

P(r/100)2*{(r/100)+3}
6) When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively, Then the total amount is given by

P ((1 + R1)/100) ((1 + R2)/100) ((1 + R2)/100)
7) Present worth of Rs. x due n years hence is given by

x/(1+R/100)

## Useful Shortcuts and Tricks for Simple Interest & Compound Interest

### Example Problems

1). Interest is compounded half-yearly, therefore,

Example:

Find the compound interest on Rs. 20,000 in 2 years at 4 % per annum, the interest is compounded half-yearly.

Solution:
Principal = Rs. 20000, Rate = 2 % per half-year, Time = 2 years = 4 half- years

Amount=Rs.21648.64

Compound Interest = Total amount – Principal

= 21648.64 – 20000

= Rs. 1648.64

2). If interest is compounded annually,

Example:

Find the compound interest on Rs. 8500 at 4 % per annum for 2 years, compounded annually.

Solution:

We are given:

Principal = Rs. 8500, Rate = 4 % per annum, Time = 2 years

= Rs. 9193.6
Compound Interest = Total amount – Principal= 9193.6 – 8500

= 693.6
Compound Interest = Rs. 693.6
3). When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively. Then, Amount (= Principal + Compound interest) = P(1 + R1/100)(1 + R2/100)(1 + R3/100).

Example:

Find the compound interest on a principal amount of Rs.5000 after 2 years, if the rate of interest for the 1st year is 2% and for the 2nd year is 4%.

Solution:

Here R1 = 2% R2 = 4% and p = Rs.5000, we have to find CI (compound interest).
CI = 5000(1 + 2/100)(1 + 4/100) – 5000
= 5000 x (102/100)(104/100) – 5000
= 5000 x (51/50) x (52/50) – 5000
= 5000 x (51 x 52/2500) – 5000
= 5000 x (2652 / 2500) – 5000
= 5304 – 5000 = 304
Hence the required compound interest is Rs.304.
4). When compound interest is reckoned half-yearly.

If the annual rate is r% per annum and is to be calculated for n years, then, in this case, rate = (n/2%) half-yearly and time = (2n) half-yearly.
Example:

Sam investment Rs.15,000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be.

Solution:

P = Rs. 15000; R = 10% p.a = 5% half-year, T = 1 year = 2 half year
Amount = Rs.16537.50

If the simple interest for a certain sum for 2yrs at the annual rate of interest R% is SI. Then,

Compound interest (CI) = SI (1+r/200)   (no. of years =2)

5). If the simple interest for a certain sum for 2 yr at 5%pa is 200, then what will be the compound interest for the same sum for the same period and the same rate of interest?

Solution:

SI =200 r=5%
CI =200(1+5/200) =200*(205/200) =205

If a certain sum at compound interest becomes x times n1^yr and y times n2^yr then,
X1/N1 = Y1/N2

## Useful Shortcuts and Tricks for Simple Interest & Compound Interest

6). If an amount at compound interest becomes twice in 5yr, then in how many years, it will be 16 times at the same rate of interest?

21/5  = 16 1/x2
=24*1/x2
1/5 = 4/x2
X2 = 5*4 =20yrs

If a certain sum at compound interest amounts to A1 in   n yrs and A2 in (n+1) yrs,
then

Rate of compound interest =(A2 – A1)/A1 *100%

Sum = A1 (A1 /A2)n

7).  A sum of money invested at compound interest amounts to 800 in 2yr and 840 in 3yrs. Find the rate of interest and the sum.

A1 =800 ; A2 =840,
Rate of interest = (840-800)/800 *100% =40/8 =5%
Sum = 800 *(800/840)2 =320000/441 = Rs.725.62

If the populations of a city P and increases with the rate of R% per annum, then

• Populations after n yr = p(1+R/100)n
• Populations n yr ago = p / (1+R/100)n

8). The population of city A is 5000. It increases by 10% in 1st year. It decreases by 20% in the 2nd yr because of some reason. In the 3rd yr, the population increases by 30%. What will be the [population of area A at the end of 3yrs?

=5000(1+10/100)(1-20/100)(1+30/100)
= 500*(11/10)*(4/5)*(13/10) = 5720

Difference between ci and si 2yr =pr2 /100

9). The difference between c.i and s.i for 2yr at the rate of 5% per annum is 5 .then the sum
5 = p (5/100)2 = Rs.2000

Rate of interest (no .of years =2)

(for only ci)
2% = 4.04%
3% = 6.09%
4% = 8. 16%
5% = 10.25%
6% = 12.36%
7%   = 14.49%
8% = 16.64%
9% = 18.81%
10%= 20.00
+ 1.00 =21%

10). What is the Compound interest for Rs. 1500 at 5% rate of interest for 2 years?
1500*(10.25/100) =153.75

### Difference between the compound interest and the simple interest

Example:

If the difference between the compound interest and the simple interest on a certain sum of money at 5% per annum for 3 years is Rs. 1220. What is the sum?
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