## Simple Interest and Compound Interest for IBPS PO

# Simple Interest and Compound Interest for IBPS PO

**Simple Interest and Compound Interest for IBPS PO, BANK, SBI PO and government exam.**

**Interest (I):** the additional amount paid by the borrower to the lender for the use of a sum of money

**Principal (P):** the sum of money lent, borrowed or invested

**Time (T): **the duration for which the sum of money is lent or invested, usually in years

**Rate (R):** the interest paid on Rs. 100 per unit of time, usually per an num (p.a.)

**Amount (A):** the sum of principal and the interest

**Simple interest:** the interest paid on the original sum of money borrowed or invested

S.I. =Principal × Rate × Time /100 i.e. I = P×R×T/100

Amount = principal + interest i.e. A = P + I

When we say, interest , it always means simple interest.

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**Compound interest:** money is said to be lent at compound interest, when the interest, which has become due at the end of a certain fixed period (one year, half year, etc., as given), is not paid to the money lender , but is added to the sum lent. The amount thus obtained becomes the principal for the next period. This process is repeated until the amount for the last period is found.

The difference between the final amount and the original principal is the required compound interest i.e.

## Simple Interest and Compound Interest for IBPS PO

** Compound Interest = Final Amount – Original Principal**

The formula for finding the amount is

A = P(1 +r/100)^{t}

And C.I. = A – P

Where A = amount

P = principal

r = rate of interest compounded yearly

t = numbers of years

When the rate for successive years are different, then

A = (1 + r1/100 ) (1 + r2/100) (1 + r3/100)……………

Where r1 %, r2%, r3% …………………. Are the rates for successive years .

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**Short tricks **

- The difference between compound interest and simple interest for some amount of money in 2 years is = P×R
^{2}/10000

- When the interest is compounded half yearly and rate of interest annually, then the amount will be after t years, A = P(1 +r/100×2)
^{t×2}

- When the interest is compounded yearly and time is 1 1/2 years, then amount will be A= P(1 +r/100)
^{1 }(1 +r/100*2)^{1}

- The compound interest for 2 years in terms of interest is , C.I. = I + I×r/100*2

- The compound interest for 3 years in terms of simple interest is

C.I. = I + I×r/100+ I/3×(R/100)^{2}

**If a sum of money becomes m times itself in t years at simple interest, then in how many years it become n times at the same rate of interest ?**

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Time = (n – 1/m – 1)t

- If a sum of money becomes m times at r% (rate of simple interest), then at what rate it becomes n times in the same time ?

Rate of interest = (n – 1/m – 1)r

- If a sum of money becomes x
_{1}in t_{1}years and x_{2}in t_{2}years, then rate of simple interest % = 100(x_{2}– x_{1})/x_{1}t_{2}– x_{2}t_{1}

- If a sum of money becomes Rs. x in t years , then the rate of compound interest is

Rate % = [(x/P)^{1/2}]×100

- If a sum of money becomes x
_{1}in t_{1}years and x_{2}in t_{2}years, then rate of compound interest % = [(x_{2}/x_{1})^{1/t1-t2 }– 1]×100

- If a sum of money becomes m times in t years, then the time taken to become mnis

Time = t×n

If difference between the S.I. and C.I. is x at the rate of r% compounded annually in 4 years , then x = P×r^{2 }(400 + r)/x×100^{4}

**For worked out Question **

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