What is the compound interest on a sum of 40,000 for 33 years at the rate of 11% per annum?

If the rate of compound interest is 20% per annum, compounded half-yearly, then what will be the interest on a principal of Rs. 1,00,000 for two years?

1. Rs. 33,100
2. Rs. 21,000
3. Rs. 46,410
4. Rs. 44,000

Answer (Detailed Solution Below)

Option 3 : Rs. 46,410

Free

CT : GK (Ancient History)

10 Questions 10 Marks 6 Mins

Rate of interest per annum = 20%, time = 2 years

⇒ Interest = P(1 + (r/2)/100)2t - P

⇒ Interest = 1,00,000[(1 + 10/100)4 - 1]

⇒ Interest = 1,00,000 [(11/10)4 - 1]

⇒ Interest = Rs. 46410

∴ Interest will be Rs. 46410.

Last updated on Oct 7, 2022

The Staff Selection Commission (SSC) has released the SSC MTS Result for the Paper I Examination which was held from 5th July to 26th July 2022. The candidates who are qualified in the SSC MTS Paper I are eligible for the Paper II, the paper II will be held on 6th November 2022. A total of 7709 vacancies are released, out of which 3854 vacancies are for MTS Group age 18-25 years, 252 vacancies are for MTS Group age 18-27 years and 3603 vacancies are for Havaldar in CBIC. 

Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!

If a sum of Rs. 40,000 at compound interest of 5 p.m amounted to Rs. 44,100. Find the time for which the money was invented.

Answer

Verified

Hint: To solve this question, first we will take all the given data from the question and then convert the rate of interest into numeric value by dividing the rate by 100, then we will substitute all the values in the formula of Compound interest $A=P{{\left( 1+\dfrac{r}{n} \right)}^{n}}$, then on solving an equation and on simplification, we will gate the value of n by comparing L.H.S and R.H.S.

Complete step by step answer:
Before we solve the question let us see what is meaning of compound interest and what the components of it are.
Compound interest just simply the addition of interest to the principal sum of a loan or deposits
The components of compound interest are as follows :
(a) Initial Principal Balance – It is the amount of loan or bond or the sum put into an investment.
(b) Interest Rate – The amount charged by a lender for the use of assets expressed as a percentage of the principal.
(c) Number of times interest is applied per time period.
(d) Number of time periods elapsed.

Now, in question, it is given that sum of Rs. 40,000 at compound interest of 5% p.m amounted to Rs.44,100.
So, we can say that the Initial Principal rate equals to Rs. 40,000. Rate of interest equals to 5% per annum and total compound interest calculated for time period ‘n’ equals to Rs. 44,100.
So, rate = $\dfrac{5}{100}$ .
We know that compound interest equals to,
$A=P{{\left( 1+\dfrac{r}{n} \right)}^{n}}$ , where A = compound Interest, P = Initial Principal balance, r = rate of interest, n = Number of times interest is applied per time period.
Putting value sin formula we get
$44,100=40,000{{\left( 1+\dfrac{5}{100} \right)}^{n}}$
On simplifying we get
$\dfrac{44,100}{40,000}={{\left( 1+\dfrac{5}{100} \right)}^{n}}$
On simplification, we get
$\dfrac{441}{400}={{\left( 1+\dfrac{5}{100} \right)}^{n}}$
Again, simplifying, we get
\[\dfrac{441}{400}={{\left( 1+\dfrac{1}{20} \right)}^{n}}\]
Solving bracket, we get
\[\dfrac{441}{400}={{\left( \dfrac{20+1}{20} \right)}^{n}}\]
\[\dfrac{441}{400}={{\left( \dfrac{21}{20} \right)}^{n}}\]
We know that ${{21}^{2}}=441$ and ${{20}^{2}}=400$
So, we can re – write above equation as
\[{{\left( \dfrac{21}{20} \right)}^{2}}={{\left( \dfrac{21}{20} \right)}^{n}}\]
On comparing, both sides L.H.S and R.H.S, we get
n = 2
So, the required time Rs 40,000 at compound interest of 5 p.m amounted to Rs. 44,100 is 2 years.

Note:
To solve such types of questions one must know the formula of compound interest which is $A=P{{\left( 1+\dfrac{r}{n} \right)}^{n}}$ and the meaning of its components. While solving, convert the rate of interest into numeric value by dividing the rate of interest by 100 and solve the equation such a way that we get the value of n by doing less calculation. Try not to make any calculation mistake.

Related Test

Answers

Related What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer?

A=P(1+R/100)^3
so
= 40000(1+11/100)^3
= 40000(111/100)^3

= 40000(1.3676)
= 54705.24 which is the amount
now CI= A - P
= 54705.24- 40000
= 14705.24 (A)

• Reply

1 Crore+ students have signed up on EduRev. Have you?

Amount after 3 years = P(1 + R/100)T
=> 40000(1 + 11/100)3
=> 40000(111/100)3
=> 40000[(111*111*111)/(100*100*100)]
=> (4*111*111*111)/100 
=> 54705.24
Compound Interest = 54705.24 - 40000 
= Rs. 14705.24

• Reply

Question Description
What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer? for Quant 2022 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2022 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer?.

Solutions for What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant. Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.

Here you can find the meaning of What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer?, a detailed solution for What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?a)Rs. 14705.24b)Rs. 14602.25c)Rs. 14822.26d)Rs. 14322.10Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Quant tests.

Related Quant Content

Download free EduRev App

Track your progress, build streaks, highlight & save important lessons and more!

A=P(1+R/100)^3 so= 40000(1+11/100)^3= 40000(111/100)^3= 40000(1.3676)= 54705.24 which is the amount now CI= A - P = 54705.24- 40000 = 14705.24 (A)

What will be the compound interest on a sum of 40000?

What is the interest received on a sum of 40000 after 2 years at a rate of interest 9 per annum?

What will be the compound interest on a sum of Rs 40000 at 6%?

What is the interest received on a sum of Rs 40000 after 2 year at a rate of compounded annually?