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Few important formula of Compound Interest:

Usually, we use the following notations,

We know, 

Now, amount after n years for compounded annually

So, Compound interest (CI) =

Let us take an example 

Find the interest of RS. 10000 at the rate of 11% per annum for 2 years compounded annually.

Solution:

From the above-mentioned formula

Here,

P = 10000 RS.

r = 11% p.a

n = 2 years

Short Tricks

P → 10000 RS.

Interest in 1st year at 11% per annum is 1100 RS.

Now for 2ND Year, interest = 1100 RS. + Interest of 1100 RS. at 11% per annum

2nd year interest = 1100 RS. + 121 RS. = 1221 RS.

Total interest after 2 year = (1100 + 1221) RS.

= 2321 RS.

Now,

Case – 1

When interest compounded half-yearly we need to take interest rate as r/2 % and time period as 2n

For that, the amount after n years interest at r% per year compounded half-yearly for a principal P is,

Example

Find the compound interest of RS. 12000 at 8% per annum for 2 years compounded half-yearly.

Solution:

Here, 

P = 12000 RS.

r = 8% per annum

n = 2 years

Compounded half-yearly,

So, after 2 years 

Case – 2

When the interest compounded quarterly we need to take the interest rate as r/4 % and the time period as 4n.

For this, the amount after n years is,

Example

Find the compound interest 14000 RS.at 8% per annum for 9 months compounded quarterly.

Solution:

Here, 

P = 14000

n = 9 months = 9/12 year = ¾ year 

r = 8%

Compounded quarterly,

Case – 3

When interest compounded monthly we need to take interest as r/12 % and time period as 12n then

Amount after n years is,

Case – 4

When the rate of interest r1% during first year r2% during 2nd year r3% during 3rd year and compounded annually. Then,

Amount after 3 years is,

Example

A man borrowed 10000 RS at 5 % p.a. for 1st year 7% per annum for 2nd year and 10% p.a. for 3rd year. Find the interest after 3 years if compounded annually.

Solution:

So, the amount after 3 years is 

Case – 5

Difference between CI and SI on a certain sum of money given for 2 years at r% per annum

Example 1 

Find the difference between SI and CI of 7000 RS given for 2 years at 10% per annum.

Solution:

P = 7000 RS.

r = 10%

t = 2 years

Example 2

Difference between SI and CI of a certain sum of money for 2 years at 5% per annum is RS 3. Find the sum.

Solution:

r = 5%

t = 2 years

Difference = RS. 3

Case – 6

Difference between SI and CI for 3 years on a certain sum of money at r% per annum

Example

Find the difference between SI and CI of 50000 RS. Given for 3 years at 10% per annum interest rate.

Solution:

P=50000 RS.

r = 10%

t = 3 years

Difference between SI and CI is,

Installments

Installments mean when the borrower pays back money to the lender in few parts then we can say that the borrower is paying in installments.

Suppose Ram borrowed 500 RS. from Shyam and Ram is paying back this 500 RS. in 5 part of RS 100

But the most important thing is that borrower also needs to pay the interest of that borrowed money of that period.

For installments in simple interest.

Then,

Where,

Example

What will be the annual Installments if the total amount of 2100 RS. Is to be paid back in 3 years at 12% simple interest.

Solution:

A = 2100 RS.

r = 12%

n = 3

Let each installment is x RS.

Then

The annual installment is 625 RS.