# Compound Interest

**Compound interest**arises when

**interest**is added to the

**principal**, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called

**compounding**.

**Note: The main difference between simple interest and compound-interest is that in case of simple interest, the principal remains the same throughout, whereas in the case of compound-interest, it goes on changing periodically.**

**Example**:

1)A bank account, for an account with $1000 initial principal and 20% interest per year would have

**Solution :**

I = P x r x t

I = 1000 x 0.2 x 1

I = $200

A = P + I

**A= $1200 at the end of 1st year.**

I = P x r x t

I = 1200 x 0.2 x 1

I = 240

A = P + I

**A= $1440 at the end of 2nd year and so on.**

Here we have counted interest on interest, but this is a bit longer method. So we will use a formula to calculate directly the amount say after 3 yrs., 4 yrs. and so on.

A = P ( 1 + r )
^{t} |

Where P = Principal

r = rate in percent

t = time period in years.

**I = Interest = A – P**

**Example**:

1) Find the compound-interest in $8000 for 2 years at 6% p.a.

**Solution :**

**Principal**= P = $8000,

**Rate**= r = 6% = 6/100 = 0.06 and

**time period**= t = 2 years

A = P ( 1 + r )^{t}A = 8000 ( 1 + 0.06) ^{2}A = 8000 (1.06) ^{2}A = 8000 x 1.1236 A = $8988.8I = A - P I = 8988.8- 8000 I = $988.80 |

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2) Find the compound interest on $24,000 at 15% p.a for 2

**⅓**years.

**Solution :**

P = $24,000, R = 15% and Time = t = 2

**⅓**

When time is in fraction then amount is given by the following formula.

**Amount after 2 ⅓ years = P ( 1 + r )**

^{2}(1 + r/3)= 24000( 1 + 0.15)

^{2}( 1 + 0.15/3)

= 24000 x (1.15)

^{2}x ( 1 + 0.05)

= 24000 x 1.3225 x 1.05

Amount = $ 33,327

∴ C.I = Amount - P

= 33,327 - 24,000

C.I = $ 9,327.

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**Compound Interest (CI)**

• Find Compound- Interest when interest is compounded Half yearly

• Find Compound- Interest when interest is compounded Quarterly

• Find CI when interest is compounded annually but Rates are different

• Finding Principal

• Finding Time Period of Investment

• Finding Rate of Interest

• Find Compound- Interest when interest is compounded Half yearly

• Find Compound- Interest when interest is compounded Quarterly

• Find CI when interest is compounded annually but Rates are different

• Finding Principal

• Finding Time Period of Investment

• Finding Rate of Interest