In simple interest,
the interest is on initial principal.
Interest remains same every year
In compound Interest,
the interest will be on total amount at the end of year
Interest changes every year
Let’s take an example
Suppose I give Rs 10,000 to Sanjay at 10% per annum interest. Find the amount after 5 years
If interest is Simple Interest
Year |
Principal |
Interest |
Amount |
Year 1 |
10,000 |
10% × 10,000 = 1000 |
10,000 + 1000 = 11,000 |
Year 2 |
10,000 |
10% × 10,000 = 1000 |
11,000 + 1000 = 12,000 |
Year 3 |
10,000 |
10% × 10,000 = 1000 |
12,000 + 1000 = 13,000 |
Year 4 |
10,000 |
10% × 10,000 = 1000 |
13,000 + 1000 = 14,000 |
Year 5 |
10,000 |
10% × 10,000 = 1000 |
14,000 + 1000 = 15,000 |
Interest = Rate × Principal
In this case, the principal remains same
So, this is simple interest.
If interest is Compound Interest
In compound interest,
The principal changes
Year |
Principal |
Interest |
Amount |
1 |
10,000 |
10% × 10,000 = 1000 |
10,000 + 1000 = 11,000 |
2 |
11,000 |
10% × 11,000 = 1100 |
11,000 + 1100 = 12,100 |
3 |
12,100 |
10% × 12,100 = 1210 |
12,100 + 1210 = 13,310 |
4 |
13,310 |
10% × 13,310 = 1331 |
13,310 + 1331 = 14,641 |
5 |
14,641 |
10% × 14641 = 1464.1 |
14,641 + 14641.1 = 16105.1 |
Here,
Interest = Rate × Principal
But Principal = Amount of previous year
Calculating compound interest like this could be difficult,
So we use formula
Amount = P (1+R/100)^n
Here,
P = Principal
R = Rate
n = Number of year
For Rs 10,000 at 10% p.a. What will be the compound interest after 4 years?
P = Rs 10,000
R = 10% p.a
T = 4 years
Amount after 4 years = P (1+R/100)^n
= 10,000 (1+10/100)^4
= 10,000 (1+1/10)^4
= 10,000 ((10 + 1)/10)^4
Let’s take some examples
For Rs 10,000 at 10% p.a. What will be the compound interest after 4 years?
P = Rs 10,000
R = 10% p.a
T = 4 years
Amount after 4 years = P (1+R/100)^n
= 10,000 (1+10/100)^4
= 10,000 (1+1/10)^4
= 10,000 ((10 + 1)/10)^4
= 10,000 (11/10)^4
= 10,000 × 14,641/10,000
= Rs 14,641
Now,
Compound Interest = Amount – Principal
= 14,641 − 10,000
= Rs 4,641
Suppose I have Rs 1000 and I put it in a bank on compound interest. What would be the amount I have after 5 years, If Interest is 5%?
Given,
P = Rs 1000
R = 5% p.a
T = 5 years
Amount = P (1+R/100)^n
= 1000 (1 + 5/100)^5
= 1000 (1 + 1/20)^5
= 1000 ((20 + 1)/20)^5
= 1000 × (21/20)^5
= 1000 × 4,084,101/3200000
= 4084101/3200
= Rs 1,276.282