Mathematics is an equally important section for CTET, MPTET, KVS & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts of the Compound Interest.

To let you make the most of Mathematics section, we are providing important facts related to the Compound Interest. At least 1-2 questions are asked from Compound Interest topic in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

**How to Overcome Exam Fever, Especially When You Fear Maths**

## Compound Interest

**Money: **Said to be lent compound interest (C.I.), if the interest is not paid as soon as it falls due but is added to the principal after a fixed period, so that the amount, at the end of the period becomes the principal for the next period.

**Note:**

- Unless there is a mention of CI, the problem should be treated as that of SI.
- the compound interest and the simple interest for one year is the same when the principle and the rate of interest are the same, provided that interest is calculated annually.
- If the interest is payable half yearly, the time is doubled and the rate become half.

For example, if the rate of interest is 10% per annum and the money is kept for 1 year, then if the rate is calculated half yearly, then r = 5% and time is 2 years.

**Important Facts and Formulae:**

If principle = Rs. P, Time = t years, Rate = R% p.a.

- When interest is compounded annually:

- When interest is compounded half – yearly Principal = Rs. P, Time = t years = (2t) half years, Rate = (R/2%) per half-yearly

- When interest is compounded quarterly:

Principal = Rs. P, Rate = R% p.a. = (R/4)% per quarter, Time = t years = (4t)quarters.

- When rate of interest is R₁%, R₂%, & R₃% for 1
^{st}year, 2^{nd}year, 3^{rd}year respectively, then Amount after 3years

**CI for two years:**

Let principle = P and rate = r% per annum

i.e. CI = 2A + B (for 2 years)

& CI for II year = A + B

**CI for three years:**

Let principal = P and rate = r% p. a.

∴ CI for (3 years) = 3A + 3B + C

CI for II year = A + B and

CI for III year = A + 2B + C

e.g. P = Rs. 1000, r = 10%

∴ A 10% of 1000 = 100

B = 10% of 100 = 10

C = 10% of 10 = 1

∴ CI for 3 years = 3A + 3B + C

= 300 + 30 + 1 = 331

- When difference between the compound interest simple interest on a certain sum of money for 2 years at R% rate is Rs. D then

Where, P = Principal

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