**Get here the Bank Exams Mock Tests Series**

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

**Simple Interest:**

**Formula**:

1) SI = P x R x T/100Â

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

Simple Interest = Principal Ã— (R1+R2+ R3â€¦..)/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 r

_{1}% for t

_{1}years, on the second part at r

_{2}% for t

_{2}years, on the third part at r

_{3}% for t

_{3}years, and so on, are equal. Then the ratio in which the sum is divided in n part is:

_{1}Ã—t

_{1}: 1/r

_{2}Ã—t

_{2}: 1/r

_{3}Ã—t

_{3}

**Example:**

**Solution:**

T1 = 5 yrÂ T2 = 6 yr

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

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

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

**Â**

**2).**Amount = Principal + S.I = p + [(p x r x t)/100]

**Example:**

**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 Ã— 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 Â 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**

**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};

^{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**

Pr

^{2}/100

^{2}or 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 + R

^{1})/100) ((1 + R

^{2})/100) ((1 + R

^{2})/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**

**Â**

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

Example:

Example:

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

**Â**

Solution:

Solution:

Amount=Rs.21648.64

Compound Interest = Total amount â€“ Principal

= 21648.64 â€“ 20000

= Rs. 1648.64

**Â**

**2).**If interest is compounded annually,

Example:

Example:

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

**Â**

**Solution:**

We are given:

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

= Rs. 9193.6Compound Interest = Total amount â€“ Principal= 9193.6 â€“ 8500

= 693.6Compound 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:

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:

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 = 304Hence 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:**Â

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:

Solution:

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

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)Â Â (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 n_{1}^yr and y times n_{2}^yr then,

**X ^{1/N1} = Y^{1/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?

2^{1/5Â }= 16 ^{1/x2}

=2^{4*1/x2}

1/5 = 4/x_{2}

X_{2} = 5*4 =20yrs

If a certain sum at compound interest amounts to A_{1} inÂ Â n yrs and A_{2} in (n+1) yrs,

then

Rate of compound interest =(A_{2} â€“ A_{1})/A_{1} *100%

**Sum = A _{1} (A_{1} /A_{2})^{n}**

**7).** Â 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.

A_{1} =800 ; A_{2 }=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 1^{st} year. It decreases by 20% in the 2^{nd} yr because of some reason. In the 3^{rd} 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 =pr^{2} /100^{2Â }Â Â

**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%Â Â = 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 interestÂ **

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

**If You Have Any Queries, Feel Free to Ask us in the below Comment Section.**