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Simple Interest

The interest calculated only on the original principal throughout the time period is called Simple Interest, that is, original principal alone produces interest. No interest is calculated on the interest generated after each time period.
 

S.I. depends on 3 factors: the principal, rate of interest and the term of loan (time period). Simple interest is directly proportional to the principal (S.I.  P). It is also directly proportional to the time period (S.I.  T ) and the rate of interest (S.I.  R).
 

Putting together the above three relations, the simple interest on a given principal P for a time period T and at a rate of interest R% is calculated using the relation,

 

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The amount A to be returned at the end of the time period is the sum of the principal P and the simple interest,

 

A = P + S.I.

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Sometimes, we have to calculate the rate of interest, when we know the amount accumulated on a principal after two different time periods. In such cases, we can find the rate of interest using the relation

 

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If two different principals are lent out at two different rates of interest, then the rate of interest on the overall principal is calculated using the relation,

 

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Example
Find the simple interest on ₹16,000 for 8 months at 3% p.a.
Solution
Clearly we can figure out by the definitions that ₹16,000 is the principal, 3% per annum is the rate and 8 months is the time period.
 
8 months is equal to 8/12 years. So, simple interest can be calculated as,
Description: 55960.png 
⇒ S.I. = ₹320

 

Example
Find S.I. on ₹50 for 6 months at the rate of 2 paise per rupee per month.
Solution
Here, rate is given as 2 paise per rupee per month. So, for 100 rupees it will become 2 × 100 paise or 2 rupees per 100 rupees.
 
Therefore, P = ₹50 R = 2% T = 6 months
 
Since, rate of interest is given with respect to months, there is no need to convert time into year.
 
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Example
How much time will it take for ₹120 to yield ₹20 as interest at 2% p.a. simple interest?
Solution
Now, interest is already given, we need to find the time period.
 
P = ₹120 R = 2% p.a. S.I. = ₹20
 
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Example
Find the rate of interest when ₹5,600 yields a simple interest of ₹500 in 2 years.
Solution
P = ₹5,600 S.I. = ₹500 T = 2 years
 
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Example
What is the sum for which the simple interest is ₹1,000 at a rate of interest 2% p.a. for 5 years?
Solution
Here principal is unknown; interest, rate and time are given.
 
S.I. = ₹1,000 R = 2% p.a. T = 5 years
 
Description: 56025.png 

 

Example
The S.I. on a certain sum is ₹10,000. The amount at the end of 10 years is ₹40,000. Find the principal.
Solution
S.I = ₹10,000 A = 40,000 T = 10 years
The time given is irrelevant here. We can simply find the principal as
Amount = Principal + S.I. ⇒ Principal = Amount – S.I.
⇒ Principal = 40,000 – 10,000
⇒ Principal = ₹30,000
 
Example
₹150 is lent out for 2 years at 15% p.a. simple interest and ₹100 is lent out for the same time period at 10%. What is the rate of interest on the entire sum lent?
Solution
Given: P1 = ₹150 P2 = ₹100
R1 = 15% p.a. R2 = 10% p.a.
We can directly apply the formula for calculating rate in case of two different principals at two different rates.
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