06 December, 2015

Simple Interest Formulas, Shortcuts and Example Problems

Quantitative Aptitude - Simple Interest

Simple Interest Basic Formulae:

Interest: Interest is some extra money added to the principal money. i.e. Extra money paid for using other's money is called Interest.

There are two types of Interests. One is Simple Interest and another is Compound Interest.

Simple Interest (S.I): If the interest on a sum or money borrowed for a certain period is reckoned uniformly, then it is called Simple Interest.

Compound Interest (C.I): Compound interest is interest added to the principal so that the added interest also earns interest from then on. This addition of interest to the principal is called compounding.

Principal (P): The Money borrowed or lent out for a certain period is called the Principal.

Let P = Principal
      R = % Rate per annum
      T = No. of years
    S.I = Simple Interest, Then

S.I. = (P * R * T)/100

P = (S.I. * 100)/(R * T)

R = (S.I * 100)/(P * T)

T = (S.T * 100)/(P * R)

Problems on Simple Interest:
1. Find the S.I. on Rs. 30,000 for 3 years at the rate interest is 6 % ?
A) Rs. 5,400          B) Rs. 5,600                 C) Rs. 5,800                 D) Rs. 6,000


Ans. A
Solution:
S.I = (P * R * T)/100
S.I = (30,000 * 6 * 3)/100
S.I = Rs. 5,400.

2. Find the Simple Interest on Rs. 5,664 at 13(3/4) % of interest for 9 months ?
A) Rs. 582.5            B) Rs. 584.1              C) Rs. 585.6                 D) Rs. 587.3


Ans. B
Solution:
S.I = (P * R * T)/100
S.I = (5,664 * (9/12) * (55/4))/100
S.I = Rs. 584.10

3. Find the S.I. on Rs. 3,125 for time 73 days at the rate of 15 % ?
A) Rs. 93.25           B) Rs. 93.50              C) Rs. 93.75                D) Rs. 93.85


Ans. C
Solution:
S.I = (P * R * T)/100
S.I = (3,125 * (73/365) * 15)/100
S.I = Rs. 93.75

4. Principal amount is Rs. 1000 and time is 2 years and S.I is Rs. 50 then what is the rate of interest ?
A) 2 %                   B) 2.5 %                    C) 3 %                         D) 5%


Ans. B
Solution:
R = (S.I * 100)/(P * T)
R = (50 * 100)/(1000 * 2)
R = 2.5 %

5. At what rate of percentage per annum will a sum of money double in 8 years ?
A) 8.5 %              B) 10 %                      C) 12.5 %                     D) 18 %


Ans. C
Solution:
R = (S.I * 100)/(P * T)
R = (P * 100)/(P * 8)
R = 12.5 %

6. In how many years, the principal amount will be thrice with 8 % of interest ?
A) 10                  B) 12.5                        C) 25                            D) 15


Ans. C
Solution:
T = (S.I * 100)/(P * R)
R = (2*P * 100)/(P * 8); Amount becomes thrice when interest equals to two times of principal.
R = 25 %

7. A Sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the Rate Interest?
A) 3 %              B) 4 %                        C) 5 %                          D) 6 %


Ans. D
Solution:
S.I = 15,500 - 12,500 = Rs. 3,000
P = Rs. 12,500; T = 4 Years
R = (3,000 * 100)/(12,500 * 4)
R = (3,000)/(125 * 4)
R = 24/4
R = 6 %

8. A Sum of Rs. 800 amounts to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3 %, it would amount to how much ?
A) Rs. 945         B) Rs. 953                  C) Rs. 987                    D) Rs. 992


Ans. D
Solution:
S.I = 920 - 800 = Rs. 120
P = Rs. 800; T = 3 Years
R = (120 * 100)/(800 * 3)
R = 5 %
New Interest Rate = 5 + 3 = 8 %
New S.I = (800 * 8 * 3)/100
New S.I = 8 * 8 * 3 = Rs. 192
New Amount = 800 + 192 = Rs. 992.

9.if the difference between interests of two banks on the principal Rs. 1000 is Rs. 20 for 1 year. Then what is the difference between Interest rates?
A) 1 %             B) 2 %                        C) 3 %                          D) 4 %


Ans. B
Solution:
S.I1 - S.I2 = Rs. 20
(1000 * R1 * 1)/100 - (1000 * R2 * 1)/100 = 20
10 * R1 - 10 * R2 = 20
(R1 - R2) = 20/10
(R1 - R2) = 2 %

10. The difference between the interests of two banks on the principal of Rs. 600 with 12 % rate is 24. Find the difference in months ?
A) 4                 B) 8                             C) 12                           D) 24 


Ans. A
Solution:
S.I1 - S.I2 = Rs. 24
(600 * 12 * T1)/100 - (600 * 12 *T2)/100 = 24
72 * T1 - 72 * T2 = 24
(T1 - T2) = 24/72
(T1 - T2) = 1/3 Years
(T1 - T2) = 4 Months.

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