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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
Let's do 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 × (4,084,101/32.00,000)
= 4084101/3200
= Rs 1,276.282