In the case of **compound profit**, the profit of any amount of principal is added to the principal at the end of each year and the total sum is considered as the new principal.

Principal of the depositor at the end of each year will go on to be increased. This increased principal is called the compound principal and the profit which is given on the increased principal is called the compound profit. Terms for giving profit may be for three months or six months or may be less than those periods.

Formula:

Compound principal C= P (1+r)

Compound profit = P (1+r)^{n} – p

Ex: If the rate of profit is10% per annum, find the compound principal of Tk. 8000 in 3 years.

Solution:

Given,

Principal, P= 8000 Taka

Rate of profit, r= 10%

Time, n= 3 years

Let compound principal = C

We know,

Compound principal C= P (1+r)^{n}

^{ }=8000× (1+10/100) = 8000× {(10+1)/10}^{3}

=8000× (11/10)^{3} = 8000×11/10×11/10×11/10= 10648

∴ Principal is 10648 Taka

Ans : 10648 Taka.

Ex: If the rate of profit is Tk. 10 percent per annum, what will be the difference of simple profit and compound profit of Tk. 5000 in 3 years?

Solution:

Simple profit:

For 100 Taka in 1 year profit is 10 Taka

∴ For 1 Taka in 1 year profit is 10/100 Taka

∴ For 5000 Taka in 3 years profit is (10×5000×3)/100 Taka

= 1500 Taka

Given, principal, P= 5000 Taka

Rate of profit, r= 10%

Time, n= 3 years

Let, compound principal= C

We know,

Compound principal C= P (1+r)^{n}

^{ } =5000× (1+10/100)

=5000×{(10+1)/10}^{3}

=5000× ( 11/10)^{3}

= 6655 Taka

∴ The compound profit= (6655- 5000) = 1655 Taka

∴ The the difference between simple profit and compound profit=(1655-1500)= 155 Taka

Ans: 155Taka.

Ex: At the rate of profit , if the compound principal of any amount of principal at the end of one year is Tk. 6500 and at the end the end of two years is Tk. 6760, what was the principal?

Solution:

Let,

Principal P

Rate of profit = r%

We know,

Compound principal C= P (1+r) ^{n+}

According to the question,

P (1+r)= 6500…………..(i)

P (1+r)^{2}= 6760…………(ii)

(ii)/ (i)

{P (1+r) ^{2}}/P (1+r) = 6760/6500

Or, 1+r= 26/25………..(iii)

From (i) and (iii) we get ,

P ×26/25 = 6500

P= 6500× 25/26

P= 6250

∴ Principal is 6250 Taka

Ans: 6250 Taka.