# Calculating Compound Interest

A sum of Rs. 24000 is borrowed by Hari for 2 years at the rate of 5% compounded annually.

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**Step 1:** Find the Simple Interest (S.I) for one year

Let the principal for the first period be

at 5% for the 1^{st} year =

**Step 2:** Then find the amount which will be paid or received. This becomes principal for the next year.

Amount at the end of 1^{st} year

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = Rs. 25200 = P_{2}

**Step 3:**Again find the interest on this sum for another one year

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = Rs. 1260

**Step 4:** Find the amount which has to be paid or received at the end of second year

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Amount at the end of 2^{nd} year = P_{2} + SI_{2
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â }= Rs. 25200 + Rs. 1260

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = Rs. 26,460

Â Â Â Â Â Â Â Â Â Â Â Â Â Total interest given = Rs. 1200 + Rs. 1260 = Rs. 2460

We can calculate SI in this way also.

When compound interest was used Hari would pay Rs. 60 more

Difference between Simple Interest and compound Interest.

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Â | Â | UnderSimple Interest |
UnderCompound Interest |

First year
Â
Â Â Third year |
Principal Interest at 10% Year end amount
Year end amount
Year end amount |
Rs. 100.00 Rs. 10.00 ------------ Rs. 110.00 ------------ Rs. 100.00 Rs. 100.00 |
Rs. 100.00 Rs. 10.00 ------------ Rs. 110.00 ------------ Rs. 110.00 Rs. 121.00 |

Interest earned by S. I. = Rs(130 - 100) = Rs. 30

Interest earned by C.I. = Rs (133.10 - 100) = Rs. 33.10

In simple Interest, the Principal remains the same

In compound Interest, the Principal charges after year.