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Compound Interest

Compound interest is computed on both the investment and the obtained interest. Compound interest is the interest that each time interest amount is paid, it is added into the principal and that also earn interest. When interest accumulated over one period is applied to the principal before computing the interest for the next period. Typical intervals are quarterly (4 times a year), monthly, daily, and continuously. Our capital will earn interest – which in itself will earn interest, which is known as compound interest. Compound interest's principal amount is investment + interest.

The annual percentage of the principal amount is represented as interest rate. The interest rate can be charged not only for year. It can be charged every month or every week or every six months. Sometimes the interest rate can be charged every day. The compound interest can be defined as the investment rate is growing exponentially and the not linearly as in the case of simple interest. The interest rate can be classified into two types

Simple interest rate
Compound interest rate

What is Compound Interest?

When interest are calculated using compound interest, they calculate interest for the whole mean period and it is add to principal and the resulted amount now serves as the principal for the next period of time. For the next period of time they calculate interest for the new principal and add it to the new principal and the resulted amount serves as the principal for the next period of time and so on. We use equation for compound interest to calculate interest for the whole mean period.

Below you could see compound interest equation:

Compound interest = A - P

Where,

A = P $\frac{1+R}{100}$

Compound Interest Definition

The compound interest can be defined as the investment rate is grows the exponentially and the not linearly grows as in the casing simple interest.

Compound Interest Formula

The formula for compound interest is given below:

Compound interest `CI=P (1+R/100) ^N`

Where,

P = Principal amount
N = Period of time
R = Rate of the interest

How to Calculate Compound Interest?

Below are the few compound interest examples which will help you to understand the method of compound interest calculation:

Solved Examples

Question 1: David paid 6000 dollars at 20% after 5 years in finance. To find the compound interest.
Solution:

Here,

Principal amount P = 6000 dollars

Period N = 5years

Interest rate R = 20%

Compound interest `CI=P (1+R/100) ^N`

`CI = 6000( 1+20/100)^5`

`=6000( 120/100 )^6`

` =6000(12/10 )^5`

`=6000(248832 / 100000)`

`= 1492992 /100`

CI = 14929.92

Total amount of compound interest = 14929.92 dollars.

Question 2: Marry paid 8000 dollars at 40% after 3 years in finance. To find the compound interest.
Solution:

Here,

Principal amount P = 8000 dollars

Period N = 3years

Interest rate R = 40%

Compound interest `CI=P (1+R/100) ^N`

`CI = 8000( 1+40/100)^3`

`=8000( 140/100 )^3`

` =8000(14/10 )^3`

`=8000(2744 / 1000)`

` = 8xx2744`

CI = 21952

Total amount of compound interest = 21952 dollars

Compound Interest Problems

Below you could see example for solving compound interest

Solved Example

Question: Charles deposited $8000 for 2 years at 6% compound interest. How much amount and also compound interest does he get after 3 years?
Solution:

Step 1: Write down the given details.

Here P = $8000, n = 2, r = 6%

Step 2: Plug it in the formula

A = P(1+i)ⁿ

A = 8000 (1 + 0.06)² = $8988.8

CI = A - P

= 8988.8 − 8000

CI = 988.8

Compound Interest Practice Problems

Practice Problems

Question 1: James deposited 4500.00 dollars for 4 years at the rate of 8% compound interest. How much amount does he after 4 years and also calculates the compound interest?

Question 2: Ricky deposited 6500.00 dollars for 6 years at the rate of 9% compound interest. How much amount does he after 6 years and also calculates the compound interest?

Continuous Compound Interest

The continuously compounded interest is the process of manipulating the interest and totaling it to already presented major amount.

Continuously compounded interest is an enormous amount when get it from the principal amount. Continuously compounded interest is specified as the receiving stable interest of the common quantity.

Continuous Compound Interest Formula

Below you could see continuous compound interest formula

A = P e^rt.

Description:

P declares Principal amount.

R declares annual interest rate.

T declares number of years.

A declares amount after time.

E declares the Napier’s number. Always it has the value of 2.7183.

Solved Example

Question: Solve and learn the compounded interest continuously after 7 years. Where the amount is $25,000 and interest rate is 3.5%.
Solution:

The principal amount = $25,000.

Interest = 3.5%.

Time = 7 years.

The continuous compound interest = P * e^rt.

= 25,000 * (2.7183)^{0.035 * 7}.

= 25,000 * 1.2776.

= 31940.585.

Simple Interest