**Compound interest :**

We might have already known the stuff "simple interest" in solving interest and investment problems. In this section, we are going to see, how to solve problems which involve compound interest (C.I).

The picture given below clearly explains the difference between compound and simple interest.

**Important Note : **

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

The formula given below can be used to find accumulated value in C.I.

**A = P(1+i)ⁿ**

A = Accumulated value (final value of an investment)

P = Principal (initial value of an investment)

**How to find the value of "i" : **

To find the value of "i", first convert the rate of interest in to decimal form. Then divide the decimal value by the number of conversion periods per year.

For example,in an investment rate of interest is 15% and compounded quarterly. First we write 15% as decimal form.That is 0.15. Now we have to divide this value by 4 (because compounded quarterly).

Finally, i = 0.15/4 = 0.0375

**How to find the value of "n" : **

n = (no. of years) X (no. of conversion periods per year)

For example, in an investment no.of years = 2 and compounded quarterly.The value of n = 2x4 = 8.

**Example 1 :**

$800 is invested in C.I where the rate of interest is 20% per year. If interest is compounded semi annually, what will be the accumulated value and C.I after 2 years ?

**Solution :**

The formula to find accumulated value in C.I is

A = P(1 + i)ⁿ

Here,

P = 800

i = 20% /2 = 0.2/2 = 0.1

n = 2 x 2 = 4

Then, the accumulated value is

A = 800(1 + 0.1)⁴

A = 800(1.1)⁴

A = 800 x 1.4641

**A = $1171.28**

C.I = A - P

C.I = 1171.28 - 800

**C.I = $371.28**

**Example 2 :**

A sum of money placed at compound interest doubles itself in 3 years. In how many years will it amount to four times itself ?

**Solution :**

Let "P" be the amount invested initially.

From the given information, P becomes 2P in 3 years.

Since the investment is in C.I, the principal in the 4th year will be 2P

And 2P becomes 4P (it doubles itself) in the next 3 years.

Therefore, at the end of 6 years accumulated value will be 4P.

Hence, the amount deposited will amount to 4 times itself in 6 years.

**Example 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 principle ?

**Solution : **

Simple interest for two years is 1200 and interest for one year 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)

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, interest 600 earned in 1st year earned this 30 in 2nd year.

It can be considered as simple interest for one year.

That is, principal = 600, interest = 30

I = Pit

30 = 600i(1)

0.05 = i

5% = i

In the given problem, simple interest earned in two years is 1200.

I = Pit

1200 = P x 0.05 x 2

1200 = P x 0.1

Divide both sides by 0.1.

1200/0.1 = P

12000 = P

Hence, the principal is $ 12,000.

After having gone through the stuff given above, we hope that the students would have understood "C.I".

Apart from the stuff given above, if you want to know more about "C.I", please click here

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...

**WORD PROBLEMS**

**HCF and LCM 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**

**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**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**