Compound Interest - Important Points
What is Compound Interest?
In compound interest, if the interest is due (not paid) after the decided time period, then it becomes a part of the principal and so is added to the principal for the next time period, and the interest is calculated for the next time period on this new principal. Interest calculated, this way is called compound interest.
The time period after which the interest is added to the principal for the next time period is called the Conversion Period.
Look at the table if we take the Principal to be 1000 and Rate to be 10%.
|
Year |
Simple Interest |
Compound Interest |
||||
|
Principal |
Interest |
Amount |
Principal |
Interest |
Amount |
|
|
1st |
1000 |
100 |
1100 |
1000 |
100 |
1100 |
|
2nd |
1000 |
100 |
1200 |
1100 |
110 |
1210 |
|
3rd |
1000 |
100 |
1300 |
1210 |
121 |
1331 |
Deductions from the above table:
a. Simple Interest earned in any year is always the same.
b. The SI and CI is same for the first year.
c. CI earned in a year keeps increasing every year.
How to calculate Compound Interest?
If Principal is P, rate of interest, R and number of interval, n , then Amount
A = P[1 + (R/100)]^n
The conversion period may be one year, six months or three months and the interest is said to be compounded, annually, semi-annually or quarterly, respectively
Compound Interest = P[1 + (R/100)]^n – P
If the rate of interest differs from year to year i.e. R1 in the first year, R2 in the second year, R3 in the third year. Then
A = P[1 + (R1/100)] x [1 + (R2/100)] x [1 + (R3/100)]