Police recruitment: Get your interest towards Simple and Compound interests

This article is in continuation to the last article on preparation for the Sub-Inspector of Police recruitment exam. Here are some practice questions and answers along with explanations on the Simple Interest and Compound Interest topic.

When a person borrows some money from another person, the lender has to sacrifice his present needs. So lender should compensate for this sacrifice. This compensation is known as interest.

Simple interest

The borrower has to pay interest according to some percent (interest rate) of principle for the fixed period of time. This percentage is known as Interest Rate. For example, the rate of interest is 10% per annum means the interest payable on Rs 100 for one year is Rs 10.

Some Basic Formulas

If A = Amount
P = Principle
I = Interest
T = Time in years
R = Rate of interest per year, then

Amount = Principle Interest

A = P I

i) Simple Interest (S.I) = P × T × R/ 100
ii) Principal P = S.I × 100/ T × R
iii) Amount A = P S.I

If a sum amount to Rs A1 in T1 years and Rs A2 in T2 years at S.I then
i) R = 100 ( A2 – A1)/ A1T2 – A2T1
and P = A1T2 – A2T1/ T2 – T1

A sum of money becomes ‘n’ times in T years at S.I then R = 100 (n-1)/ T and T = 100 (n-1)/R

Compound Interest

In Compound Interest, every year interest value is added to principle and then interest is calculated on the amount.

To understand compound interest clearly, let’s take an example

Ram borrowed Rs 1000 from Sham for 3 years. What will be the interest value?

Difference between simple interest and compound interest

After three years, in simple interest, the total amount would be 1300
And in compound interest, the total amount would be 1331.
Some Basic Formulas

If A = Amount
P = Principle
C.I. = Compound Interest
T = Time in years
R = Interest Rate per Year

Formulae:

i) If the interest is compound annually then A = P (1 R/100) T
ii) If the interest is compound half-yearly then A = P [1 (R/2)/100] 2T
iii) If the interest is compound quarterly then A = P[ 1 (R/4)/100] 4T
If the interest is compound annually but time is in fraction say 53/2 years then Amount

A = P (1 R/100) 5 × (1 3/2R/100)

If the rates are different for different years, say R1% , R2%, R3% for 1st , 2nd, 3rd years respectively then Amount = P (1 R1/100)(1 R2/100)(1 R3/100)

Present worth or present value of Rs x due in years hence is given by

Example 1:
Find the simple interest on Rs 7000 at 50/ 3% for 9 months

Solution:
S.I. = (P × R × T /100
= (7000 × 50 × 9 /3× 12 × 100 = 875

Example 2:
If A lends Rs 3500 to B at 10% p.a. and B lends the same sum to C at 11.5% p.a., then the gain of B (in Rs) in a period of 3 years is

Solution:
Gain of B = (3500 × 11.5 × 3/100) – (3500 × 10 × 3/100 ) = 157.50

PRACTICE QUESTIONS:

1. Neha borrows Rs 4000 from a bank for a period of 3 years at the rate of 15% p.a. What is the amount to be repaid to the bank?
A. 1800 B. 18000 C. 5800 D. 58000
Ans: C

Explanation:
Let Principal = P, R = Rate of Interest per Annum, T = Time in years
P = 4000; t = 3; r = 15%
Simple Interest = P × T × R/100 = 4000 × 3 × 15/100 = 1800
Amount to be repaid to the bank = P S.I = 4000 1800 = 5800

2. A sum of money triples itself in 16 years at simple interest. What is the rate of interest
A. 12½% B. 15½% C. 9% D. 9½%
Ans: A

Explanation:
Assume that the principle = P
Money triples in 16 years then A = 3P
S.I = Amount – Principle = 3P – P = 2P
R = 100 × S.I/ (P × T)
=100 × 2P/ (P × 16)
=25/2 = 12.5 %

By Banda Ravipal Reddy
Director, SIGMA
Sai Institute of General Mental Ability
Hyderabad