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Concepts: Simple Interest Notes | Study Quantitative Aptitude for Competitive Examinations - Quant

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Simple Interest:

Formula:

1) SI = P x R x T/100 

2) Principal = Simple Interest ×100/ R × T

3) Rate of Interest = Simple Interest ×100 / P × T

4) Time = Simple Interest ×100 / P × R

5) If rate of Simple interest differs from year to year, then

Simple Interest = Principal × (R1+R2+ R3…..)/100

The four variables in the above formula are:
 SI=Simple Interest
 P=Principal Amount (This the amount invested)
 T=Number of years
 R=Rate of interest (per year) in percentage

 

1). A sum of money is divided into n parts in such a way that the interest on the first part at r1% for t1 years, on second part at r2% for t2 years, on third part at r3% for t3years and so on, are equal. Then the ratio in which the sum is divided in n part is:

1/r1×t1: 1/r2 ×t2: 1/r3×t3

Example:

A sum of Rs 7700 is lent out in two parts in such a way that the interest on one part at 20% for 5 yr is equal to that on another part at 9% for 6 yr. Find the two sums.

Solution:

Here, R1 = 20% R2 = 9%

T1 = 5 yr T2 = 6 yr

By using formula, ratio of two sums  = 1/100 : 1/54 = 27 : 50

Therefore, first part = [27/(27+50)]*7700 = Rs 2700

Second part = [50/(27+50)]*7700 = Rs 5000

 

2). Amount = Principal + S.I = p + [(p x r x t)/100]

Example:

What Principal will amount to Rs. 16000 in 6 years at 10% simple interest?

Solution:

Let the principal be Rs. p, given rate of interest is 10% and time = 6 years.
 Amount received at the end of 6 years = 16000 Rs.
 => 16000 = p + (p x 10 x 6)/100 = p + 6p/10 = 16p/10 => P = 16000 x (10/16) = 1000 x 10 = 10000 Rs.
 Principal should be Rs. 10000

3). If sum becomes n times in T yr at simple interest, then formula for calculating rate of interest
R =100(n-1) /T %
4). A sum of money becomes 4 times in 20 yr at SI. Find the rate of interest?
 R =100(4-1)/20
 =100*3 / 20 =5*3 =15
5). If A sum becomes n times in at certain rate of interest .then the time taken in                    which the same amount will be n times at the same rate of interest:
= (n-1)/2 × T (n = number of times)

6). If A sum becomes 3 times in at certain rate of interest in 5years .find the time taken in  the same amount will be 8 times at the same rate of interest:
 =(8-1)/2*5
 = 7/2 * 5
 =17.5years

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