**Difference between simple and compound interest worksheet :**

Worksheet on difference between simple and compound interest is much useful to the students who would like to practice solving word problems on simple and compound interest.

1. The difference between the compound interest and simple interest on a certain investment at 10% per annum for 2 years is $631. Find the value of the investment.

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

3. The compound interest and simple interest on a certain sum for 2 years is $ 1230 and $ 1200 respectively. The rate of interest is same for both compound interest and simple interest and it is compounded annually. What is the principal ?

**Question 1 : **

The difference between the compound interest and simple interest on a certain investment at 10% per annum for 2 years is $631. Find the value of the investment.

**Answer :**

The difference between compound interest and simple interest for 2 years is 631.

Then we have,

P(R/100)² = 631

Plug R = 10

P(10/100)² = 631

P(1/10)² = 631

P(1/100) = 631

Multiply both sides by 100

P = 631 x 100

P = 63100

Hence, the value of the investment is $63100.

**Question 2 : **

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

**Answer :**

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 s $1000.

**Question 3 : **

The compound interest and simple interest on a certain sum for 2 years is $ 1230 and $ 1200 respectively. The rate of interest is same for both compound interest and simple interest and it is compounded annually. What is the principal ?

**Answer :**

To find the principal, we need rate of interest. So, let us find the rate of interest first.

**Step 1 : **

Simple interest for two years is $1200. So interest per year in simple interest is $600

So, C.I for 1st year is $600 and for 2nd year is $630.

(Since it is compounded annually, S.I and C.I for 1st year would be same)

**Step 2 : **

When we compare the C.I for 1st year and 2nd year, it is clear that the interest earned in 2nd year is 30 more than the first year.

Because, in C.I, interest $600 earned in 1st year earned this $30 in 2nd year.

It can be considered as simple interest for one year.

That is principle = 600, interest = 30

I = PRT / 100

30 = (600 x R x 1) / 100

30 = 6R

Divide both sides by 6.

30/6 = R

5 = R

So, R = 5%

**Step 3 : **

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

= 1230 - 1200

= 30

Then we have,

P(R/100)² = 30

Plug R = 5

P(5/100)² = 30

P(1/20)² = 30

P(1/400) = 30

Multiply both sides by 400

P = 30 x 400

P = 12000

Hence, the principal is $12000.

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

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