Simple Interest - Aptitude test, questions, shortcuts, solved example videos

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Simple Interest

Points to Remember

1) Simple Interest: If the interest on a sum borrowed is reckoned uniformly, for a certain period, then it is called as simple interest. It is a quick method of calculating interest charged on a loan. Simple interest can be easily determined by multiplying the interest rate by principal by the number of periods.
2) Principal: It is the money borrowed or lent out for a certain period of time.
3) Interest: Rate of money paid regularly for using money on lent.
4) Total amount: Sum of principal and simple interest.

Important Formulae:

Simple interest on principal amount P for T years at the rate of R % is given as:
1) Principal = 100 × S.I.
(R × T)
2) Years = (100 × S.I.)
(P × R)
3) Rate of Interest = (100 × S.I.)
(P × T)
4) Simple Interest = (P × R × T)
100

Quick tips and tricks

1) The rate of interest is always calculated per year unless specifically noted.

2) If in any numerical, the time given is specified in months, then convert it into years by simply dividing number of months by 12. If time is given in days, then convert days into year by dividing it with 365.
a) S.I. = (P × R × M)
1200
( Here rate of interest is given in percent and time in months (M))
b) S.I. = (P × R × D)
36500
( Here rate of interest is given in percent and time in days (D))

3) Principal is the amount deposited or borrowed, so do not get confused between such terms.

4) Simple Interest = Principle x Rate of Interest X Time
a) S.I. = PRT ------------------- (If rate of interest is in decimal form)
b) S.I. = (P × R × T)----------- (If rate of interest is in percent form)
100

5) If sum of money becomes (z times) in (T) years at simple interest, then rate of interest (R) can be calculated using the formula:
Rate of Interest (R) % = 100 (z – 1)
T

6) If sum of money becomes (z times) at rate of interest (R) % per annum at simple interest, then time (T) can be calculated using the formula:
Time (T) = 100 (z – 1)
R


Different types of questions asked in this chapter

Generally 3 basic types of questions discussed below are asked in the exams. Understanding and studying theses concepts will help in solving numerical related to this chapter.

Type 1: Find simple interest


Q 1. What will be the simple interest on Rs. 80,000 at 16(2/3) % per annum for 9 months?

a. 8,000
b. 9,000
c. 10,000
d. 11,000
View solution

Correct Option: (c)

We are given:
1) Principal = Rs. 80,000

2) Rate of interest = 162 %
3
3) Time = 9 months
Rate of interest = 162 % = 50
33
Time = 9 = 3 years
124
Simple Interest = (P × R × T)
100

Substituting the given values, we get
Simple Interest = 80,000 × 50 × 3
10034

Simple Interest = Rs.10,000


Q 2. Find the simple interest on Rs. 5000 at 6 % per annum for the period from 5th Feb to 19th April, 2015.

a. Rs. 40
b. Rs. 50
c. Rs. 60
d. Rs. 70
View solution

Correct Option: (c)

We are given:
1) Principal = Rs. 5000
2) Rate of interest = 6 %
3) Time = 5th Feb to 19th April, 2015

First find the time period 5th Feb to 19th April, 2015
Feb = 28 – 5 = 23 days
March = 31 days
April = 19 days
Total days = 23 + 31 + 19 = 73 days
Convert days into years, by dividing it by 365

Time = 73 = 1
3655
Simple Interest = (P × R × T)
100
= [5000 × 6 × (1/5)]
100
=Rs.60

Simple Interest = Rs. 60


Q 3. Suresh borrows Rs. 10,000 for 2 years at 4 % p.a. simple interest. He lends it to Ramesh at 6 % p.a. for 2 years. Find his gain in this transaction per year.

a. Rs. 150
b. Rs. 200
c. Rs. 400
d. Rs. 450
View solution

Correct Option: (b)

We have to calculate the gain in 2 years.

1) In case of Suresh

S.I.10000 × 4 × 2 = Rs. 800
100

2) In case of Ramesh
S.I.10000 × 6 × 2 = Rs. 1200
100

Suresh has a pay a simple interest of Rs. 80 to the person from whom he borrowed Rs. 1000 and Ramesh has to pay Rs. 120 to Suresh.
Hence, gain in 2 years = 1200 – 800 = Rs. 400

But we are asked to find gain of Suresh per year. Therefore,
Gain in 1 year = 400 / 2 = Rs. 200

Type 2: Find rate of interest


Q 4. At what rate percent per annum will sum of money double in 20 years?

a. 1.2 %
b. 2 %
c. 4 %
d. 5 %
View solution

Correct Option: (d)

Hint: If sum of money becomes (z times) in (T) years at simple interest, then rate of interest (R) can be calculated using the formula:

Rate of Interest (R) % = 100 (z – 1)
T
Here, principal amount is not given.
Hence, we can directly use the trick to calculate the rate of interest.
Rate of Interest (R) % = 100 (2 – 1)
20
Rate of Interest (R) %=5 % p.a.

Alternate solution
Let Principle = P, then S.I. = P
P = (P × R × T)
100
R = (P × 100) = 100 = 5 % p.a.
(P × T)20


Q 5. John took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If he paid Rs. 540 as interest at the end of loan period, what was the rate of interest?

a. 2 %
b. 3 %
c. 4 %
d. 6 %
View solution

Correct Option: (d)

Simple interest is same as the rate of interest.
Hence,
Rate of interest = R% and Time = R years

S.I. = (P × R × R)
100
60 = (1500 × R2)
100
15R2 = 540
R2 = 36
R=6 %
Rate of Interest = 6 %


Q 6. A sum of Rs. 12,000 amounts to Rs. 15,000 in 4 years at the rate of simple interest. Find the rate of interest.

a. 6.25 %
b. 4.25 %
c. 5.9 %
d. 5 %
View solution

Correct Option: (a)

A Sum of Rs. 12,000 amounts to Rs. 15,000 in 4 years, at the rate of simple interest.
This means that the after 4 years, the principal amount increases to Rs. 15000.

Therefore,
S.I. = Rs. 15000 – Rs. 12000
S.I. = Rs. 3000

Rate of Interest = (100 × S.I.)
(P × T)
= (100 × 3000)
(12000 × 4)
= 6.25 %
Rate of Interest = 6.25 %

Type 3: Find principal or amount


Q 7. Nikhil borrowed some money at the rate of interest 5 % p.a. for first 2 years, 8 % p.a. for next 5 years and 10 % p.a. for a period beyond 7 years. If he pays total interest of Rs. 8000 at the end of 10 years, then find the money Nikhil borrowed.

a. Rs. 40,000
b. Rs. 35,000
c. Rs. 25,000
d. Rs. 10,000
View solution

Correct Option: (d)

We are given,
1) Nikhil borrowed some money at the rate of interest 5 % p.a. for first 2 years.
2) 8 % p.a. for next 5 years
3) 10 % p.a. for a period beyond 7 years.
4) He pays total interest of Rs. 8000 at the end of 10 years

Therefore, considering these 4 points, we can form a simple equation to find the money borrowed.
Let the principal/money borrowed be x.

4) Simple Interest = (P × R × T)
100
Total Simple Interest paid at the end 10 years= S.I.paid in 1st 2 years+S.I.paid in 1st 5 years+ S.I.paid in remaining 3 years
8000 = (x × 5 × 2) + (x × 8 × 5) + (x × 10 × 3)
100100100
8000 = (10x) + (40x) + (30x)
100100100
800000=80x
x=Rs.10,000
The money borrowed by Nikhil = Rs. 10,000


Q 8. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 2 % higher rate, it would have fetched Rs. 400 more. Find the sum.

a. 8000
b. 9000
c. 10000
d. 12000
View solution

Correct Option: (c)

Let sum be x.
Original rate be R.
1st condition:
Rate of interest = R
Time = 2 years
2nd condition:
Rate of interest increased by 2 = (R + 2) %
Time = 2 years
Therefore,

[P × (R + 2) × 2] – (P × R × 2) = 400
100100
2PR+4P-2PR- =40000
4P=40000
P=Rs.10000
The required sum is Rs. 10,000


Q 9. The S.I. on a certain sum of money for 4 years at 15 % per annum is Rs. 180 more than S.I. on same sum for 5 years at 10 % per annum. Find the sum.

a. 1000
b. 1200
c. 1800
d. 2000
View solution

Correct Option: (c)

Let the sum be P.
As the S.I. on sum of money P for 4 years at 15 % is Rs. 180 more than S.I. on same sum P for 5 years at 10 %.

(P × 15 × 4) – (P × 10 × 5) = 180
100100
6P – 5P = 180
1010
P=Rs.1800
The required sum is Rs. 1800


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