Deducing a Formula for Compound Interest
Zubeda asked her teacher, ‘Is there an easier way to find compound interest?’ The teacher said ‘There is a shorter way of finding compound interest. Let us try to find it.’
Suppose
Let
(1)
So,
= ₹ 5000
(2)
= ₹
₹ 5000
=
=
=
Proceeding in this way the amount at the end of n years will be
A = P
So, Zubeda said, but using this we get only the formula for the amount to be paid at the end of n years, and not the formula for compound interest.
Aruna at once said that we know CI = A – P, so we can easily find the compound interest too.
Example 8: Find CI on ₹ 12600 for 2 years at 10% per annum compounded annually.
Solution: We have
A = P
₹ 12600
₹ 12600
CI = A - P = ₹
TRY THESE
- Find CI on a sum of Rs. 8000 for 2 years at 5% per annum compounded annually.
To find the compound interest (CI) on a sum, we can use the formula:
CI =
Where: P is the principal amount (Rs.
First, calculate the amount after 2 years using the formula:
A =
= 8000 ×
Now, find the compound interest:
CI = A − P =
So, the compound interest on Rs. 8000 for 2 years at 5% per annum is Rs. 820.