**Difference between compound and simple interest for 3 years :**

In this section, we are going to see, how to find the difference between compound interest and simple interest on a certain principal for three years.

The formula given below can be used to find the difference between compound interest and simple interest for three years.

The above formula is applicable only in the following conditions.

1. The principal in simple interest and compound interest must be same.

2. Rate of interest must be same in simple interest and compound interest.

3. In compound interest, interest has to be compounded annually.

**Example 1 :**

$800 is invested in both simple interest and compound interest at the same rate of interest for three years. If the rate of interest is 20%, find the difference between compound interest and simple interest.

**Solution :**

The formula for difference between compound interest and simple interest for three years is

C.I - S.I = P(R/100)²(R/100 + 3)

In the above formula, plug R = 20, P = 800

C.I - S.I = 800(20/100)²(20/100 + 3)

Simplify

C.I - S.I = 800(1/5)²(1/5 + 3)

C.I - S.I = 800(1/25)(16//5)

C.I - S.I = 800 x 16/125

C.I - S.I = 800 x 16/125

C.I - S.I = 102.40

Hence, the difference between compound interest and simple interest is $102.40.

**Example 2 :**

The difference between the compound interest and simple interest on a certain principal is at 10% per year for 3 years is $31. Find the principal.

**Solution :**

The difference between compound interest and simple interest for three years is 31.

Then we have,

P(R/100)²(R/100 + 3) = 31

Plug R = 10

P(10/100)²(10/100 + 3) = 31

P(1/10)²(1/10 + 3) = 31

P(1/100)(31/10) = 31

P(31/1000) = 31

Multiply both sides by 1000/31

P = 31 x (1000/31)

P = 1000

Hence, the principal is $1000.

After having gone through the stuff given above, we hope that the students would have understood "Difference between compound interest and simple interest for 3 years".

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