Introduction
First, we know the basic things related to "simple interest" chapter.
Principal:-
It is the money that a person takes in the form of a loan from any person or bank or other financial institutions. This is denoted by P.
Rate:-
Each loan is given at a fixed rate, usually expressed in percentages. This is denoted by r.
Time:-
The money taken as a loan is payable after a certain period. This period is called time. This is denoted by t.
Interest:-
The borrower pays some amount in addition to the principal amount after the expiry of the period. This extra amount is called interest. This is denoted by I.
Amount:-
This is the entire amount that is to be returned by the borrower. Obviously, this would include both principal and interest. This is denoted by A.
Some Formula:-
1. . 2. .
3. . 4. .
5. . 6. .
Some Example
1. A sum of money becomes of itself in 3 years at a certain rate of simple interest. The rate of interest per annum is:
a).
b).
c).
d).
Ans: -
Here I= P.=P.
So, r = .
2. In how many years the simple interest of the principal amount 400 at per annum will be Rs. 100?
Ans: - Time = years.
Note:-
1. Simple interest has a proportional relationship with P, t, and r. When only P is changed by n or by then S. I. also changes in the same ratio.
For example, if P is doubled, then S.I. will also be double. If it is increased by then S.I. will also increase by provided r and t are constant.
2. When P is increased by m times, r is increased by m times, and t is increased by q times then S.I. is increased by . Similar to the case of decrease.
Trick:- 1
A sum of money n multiplies in t years at the rate of simple interest.
So rate of interest =
Example:-
1. A sum of money becomes nine times in 12 years. What is the simple interest rate per annum?
Ans:- rate of interest =
= =
Trick:- 2
A sum becomes n times at the rate of at simple interest then time
t = .
Example:-
1. A sum of money becomes 16 times at the rate of per annum. For how long was that amount lent at simple interest?
Ans:- time = = 180years.
Trick:- 3
# If the sum is n times in t years then it will be m times in years. As the rate of interest is constant.
# If the sum is n times in rate of interest then it will be m times in rate of interest. As time is constant.
Example:-
1. A sum becomes 5 times in 3 years. In how many years it will be 10 times?
Ans:- time = = years.
2. If a sum becomes 4 times with per year simple interest, then find the rate of simple interest for which the sum will be 6 times at the same time.
and:- rate = = .
Trick:-4
The sum of money was given for a certain period of time t at the rate of per annum. If it is given at the rate of per annum then interest will be x rupees more or less,
Here the principle is = .
Example:-
1. A sum of money lent at 4% per annum for 3 years. If that amount had been paid at the rate of 5.5% per annum, Rs. 1800 would have received more interest. What was that amount?
Ans:- The principle is
= = 40000.
Trick:-5
If the sum will be A in t years and it will be B in s years, then sum = A - .
Example:-
If some money will be 500 in 3 years and 700 in 5 years. Find the money.
Ans:- principle = 500 -
= 500 - .
= 500 - 300 = 200.
Trick:-6
The simple interest on an amount is that of the principal. If the rate of interest per annum and the time are the same. Then time = rate per annum =
.
Example:-
If the simple interest on a sum is of the principal and the rate of interest and the time are the same, then what is the annual rate of interest?
Ans:- the rate of interest= =
= .
Trick:-7
The rate on a sum of money P is r% for the first t years, s% for the next f years, and c% for the next b years and the total interest is x then the principal = .
Example:-
The rate on a principal is 3% for the first 2 years, 5% for the next 3 years, and 6% for the next 2 years, and the total interest at the end of seven years is Rs.660. If so, what is that principle?
Ans:- principal = = 2000.
Trick:-8
A sum P is divided into two parts in such a way that the interest on the first part at the rate of r% for t years is the same on the second part at the rate of s% for c years. In this case, we get,
.
Example:-
Rs.3600 Rs. was divided into two parts in such a way that interest on the first part at 6% rate in 2 years, the second part at 8% rate in 3 years yields equal interest. What is the share of the principal given the rate of 8%?
Ans:- .
So, 2nd part = = = 1200.
Trick:-9
A sum of money out to P is lent at the rate of r% per annum and the rest at the rate of s% per annum. If the total interest received after t year is m. then the loan amount, which was given at the rate of s%
= .
And the loan amount, which was given at the rate of r%
= .
Note:- negative sign neglect.
Example:-
If one part of 6000 rupees was lent at the rate of 4% per annum and the rest at the rate of 7% per annum. If after 3 years Rs. 900 interest comes, then how much Rs. lent at the rate of 4%.
Ans:- loan amount =
= -4000
= 4000 (neglect negative sign).
Trick:- 10
If m amount given in t instalment with rate of interest per annum, then the amount of each instalment is
= .
Example: -
The amount 3052 payable in 4 installments when the interest rate is 6% per annum, then find the instalment.
Ans: - The instalment
=
=
=
= 700.
Some Important Example: -
1. Rs. 500 was invested at 12% per annum simple interest and a certain sum of money invested at 10% per annum simple interest. If the total interest on both the sum after 4 years is Rs. 480, the latter sum of money is :
(a) Rs. 450 (b) Rs. 750 (c) Rs. 600 (d) Rs. 550
2. A money lender finds that due to fall in the annual rate of interest from 8% to , his yearly income diminishes by Rs. 61.50. His capital is
(a) Rs. 22400. (b) Rs. 23800
(c) Rs. 24600. (d) Rs.26000
3. A lends Rs. 2500 to B and a certain sum to C at the same time at 7% annual simple interest. If after 4 years A received interest of Rs. 1120 from B and C, the sum lent to C is
(a) Rs. 700. (b) Rs. 6500
(c) Rs. 40000. (d) Rs. 1500
4. A certain sum of money amounts to Rs. 756 in 2 years and to Rs. 873 in years at a certain rate of simple interest. The rate of interest per annum is
(a) 10%. (b) 11%. (c) 12%. (d) 18%
5. What sum will amount to Rs. 7000 in 5 years at simple interest?
(a) Rs. 6300 (b) Rs. 6500
(c) Rs. 6000. (d) Rs. 5000
6. A sum of money becomes itself in year at a certain rate of simple interest. The rate of interest per annum is
(a) 10%. (b) 1% (c) 2.5%. (d) 5%.
7. The simple interest on a certain sum for 8 months at 4% per annum is Rs. 129 less than the simple interest on the same sum for 15 months at 5% per annum. The sum is:
(a) Rs. 2,580. (b) Rs. 2400.
(c) Rs. 2529. (d) Rs. 3600
8. A man loses Rs. 55.50 yearly when the annual rate of interest falls from 11.5% to 10%. His capital (in rupees) is
(a) 3700. (b) 7400. (c) 8325. (d) 1110
9. A sum of Rs. 1000 is lent out partly at 6% and the remaining at 10% per annum. If the yearly income on the average is 9.2%. the both parts respectively are:
(a) Rs. 400, Rs. 600. (b) Rs. 450, Rs. 550. (c) Rs. 200, Rs. 800 (d) Rs. 550, Rs. 450
10. A man took a loan from a bank at the rate of 12% per annum at simple interest. After 3 year he had to pay Rs. 5400 as interest only for that period. The principal amount borrowed by him was:
(a) Rs. 2000 (b) Rs. 10,000
(c) Rs. 20,000. (d) Rs. 15,000
11. A sum of money at simple interest amounts to 1,012 in year and to Rs. 1067.20 in 4 years. The rate of interest per annum is :
(a) 2.5% (b) 3%. (c) 4% (d) 5%
12. A sum of money lent out at simple
interest amounts to Rs. 720 after 2 years and to Rs 1020 after 5 years. The sum is
(a) Rs. 520. (b) Rs. 600
(c) Rs 700. (d) Rs. 710
13. The sum of money, that will give Rs. 1 as interest per day at the rate of 5% per annum simple interest is:
(a) Rs. 3650. (b) Rs. 36500
(c) Rs. 730. (d) Rs. 7300
14. Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was Rs. 760, what amount was lent in each case ?
(a) Rs. 1700. (b) Rs. 1800
(c) Rs. 1900. (d) Rs. 2000
15. Simple interest on a certain sum at a certain annual rate of interest is of the sum. If the number representing rate percent and time in years be equal, then the rate of interest is :