How to find out Compound Interest quickly

We all are familiar with the conventional formulae of simple Interest and Compound Interest.

Let us pick up a question do it by conventional method.

Find the compound Interest on Rs.5000 at 12% per annum for 2 years, compounded annually ?Solution:                

P = 5000
R= 12
T = 2 years

Now as you can see that if you go by the formula, it is very tedious task .Instead of using formula, let us learn the quick way to solve this problem, we can go by the percentage concept and get the required answer.We all know that while calculating the compound interest , we get interest not only on the principal amount but also on the previous years’ interest .

Let us find out the total compound interest and understand this technique :
In the first year we get interest only on principal amount

Let us make it in a formula.

Suppose interest for first year be A and interest for second year is B , then the formula could be like:

After getting the percentage of compound interest, we can find out the compound interest from the principal. Let us try some questions:
• Find the compound interest on a sum 6000 at 15% per annum for 2 years? 
Now with this percentage we can directly find out the compound interest.

Required Compound interest = 32.25% of 6000 =1935

What if the number of years is 3.

• Find the compound interest on a sum of Rs. 9000 at 10% per annum for 3 years. 

So in case if the number of year is 3 we will calculate for 2 years then we will follow the same procedure with 3rd year.

Compound Interest for 2 years 

Ques 1.

A person gives a discount of a% and then he gives discount of b%. Find equivalent discount.

Sol.

Ques 2.

Find equivalent discount of 20% and 30%.Sol. 

Ques 3.

A shopkeeper wants to sell his defective items. The mrp of each item is Rs 500. He gives a discount of a % and an additional discount of 10% and sells the item at a price of Rs 360. Find value of a.
Sol.

Ques 4.

The MRP of a bicycle is Rs.3000. The shopkeeper first gave discount of 35% and then discount of 20%. Find the price at which one would purchase that bicycle.
Sol.

Ques 5.

A shopkeeper gives 3 successive discounts of 12 %, 11 % and 10%. Find equivalent discount.
Sol.

Compound Interest for 3 years

Ques 1.

A sum of Rs.36000 is invested at rate of   for 1 year and 73 days. Find the interest earned in the last 73 days.
Sol:

Ques 2.

A sum of 10000 is invested for a period of 3 years at a rate of 10%. Find the amount.
Sol: 

Ques 3.

A sum of Rs.64125 is invested for a period of 3 years at a rate of  CI per annum. Find the total interest accrued in the 3rd year.
Sol: 

Ques 4.

Rahul invests a sum of Rs.49392 is invested for a period of 3 years at rate of  CI per annum. But Sachin invests the same sum at same rate at rate of simple interest for same period. Find How much Rahul will get more than Suresh.
Sol:

Ques 5.

A certain sum is invested for 3 years at 15% rate of interest. If the difference between compound interest and simple interest is Rs. 1701, find the principal
Sol: