**Difference between Simple and Compound Interest**

Simple interest is only based on the principal amount of a loan, while compound interest is based on the principal amount and the accumulated interest.

We can explain the difference between simple interest and compound interest in simple words as given below.

Principal is always constant and it will never change. |
Principal is a variable and it will be changing for each term. |

$1000 is invested at 10% simple interest and 10% compound interest where the interest is compounded annually.

The picture given below explains the difference between simple interest and compound interest for the above investment.

**Important Note : **

When we look at the above picture, it is clear that interest earned in simple interest and compound interest is same ($100) for the 1st year when interest is compounded annually in compound interest.

The above two formulas are 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.

**Question 1 : **

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

**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

(31/10)

= 31

Multiply both sides by 1000/31

P = 31 x (1000/31)

P = 1000

Hence, the principal is $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 two 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".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**