Basic Concepts and Definitions:-
Simple Interest (SI):-
Simple Interest is a quick and easy method of calculating the
interest charged on a loan or deposit.
Principal:- The original sum of
money loaned or deposited is known as Principal.
It is denoted by ‘P’.
Interest:- The amount of money
that is to be paid for borrowing money or that is earned on a deposit is known
as Interest. It is denoted by
‘I’.
Time:- The duration for
which the money is borrowed or deposited is called Time. It is generally denoted by ‘T’. Sometimes it is
denoted by ‘n’.
Rate of Interest:-
The percent of interest that is to be paid for money borrowed, or
earned for money deposit is known as Rate
of Interest. It is denoted by ‘R’.
Amount:- The sum of Principal
and Interest is known as Amount. It is denoted by ‘A’.
Amount = Principal + Interest
Formula:- Interest = {(Principal × Rate of Interest × Time) / 100}
Symbolically, I = {(P × R × T) /
100}
Q. A sum of Rs. 700 is put at simple interest at a rate of 5% for 3 years. Calculate the Interest. Also determine the Amount.
Ans. I = {(700 × 5 × 3) / 100} = Rs. 105
Amount = Rs.(700 + 105) = Rs. 805
Tricks Relating
Problems on Simple Interest:-
1.
If a sum of money becomes x
times in n years at simple rate of
interest, then the time (n) = {100 × (x - 1) / R}
Ex. If a sum of money becomes 3 times at a rate
of interest of 10%. Determine the time.
Ans. n = {100 × (3 - 1) / 10} = 20 years
2. If a sum of money becomes x times in n years at simple interest,
then the rate is calculated as R = {100 × (x – 1) / n}%
Ex. A sum of money becomes 3 times
in 25 years at simple interest. Calculate the rate of interest.
Ans. R = {100 × (3 – 1) / 25}
= 8%
3. If the interest on a money is 1/x of the principal and the number
of years is equal to the rate of interest then rate of interest = √(100 / x)
Ex. If the interest on a money is 1/36 of the principal and the
rate of interest is equal to the number of years. What is the rate of interest?
Ans. R = √(100 / 25) = 2%
4. A sum was put at simple interest at a certain rate for n years. If
the sum would have put at a r% higher rate, it could yield Rs. x more. In this
case the Principal = {100 × x / (n × r)}.
Ex. A sum was put at simple
interest at a certain rate for 2 years. If the sum would have put at a 5%
higher rate, it would have yield Rs. 1000 more. Determine the principal.
Ans. P = {(100 × 1000) / (5
×2)} = Rs. 10000
5. The rate of interest for t1 years is r1%, t2
years is r2%, t3 years is r3%. If a man gets
interest of rs. x for (t1 + t2 +t3 = t) years,
then the principal = {100 × x / (r1t1 + r2t2
+ r3t3)}
Ex. The rate of interest for 2
years is 5%, 3 years is 6% and 4 years is 4%. If a man gets interest of rs.
8800 for 9 years, calculate the principal amount.
Ans. P = [{8800 × 100 / {(2 ×
5) + (3 × 6) + (4 × 4)}] = {8800 × 100 / 44} = rs. 20000
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