Quantitative Aptitude

Simple and Compound Interest

3,394 Questions
All Simple interest and its inverse forms 768 Compound interest with annual compounding 742 Simple-interest growth and split sums 626 Difference between compound and simple interest 479 Half-yearly and quarterly compounding 252 Changing rates and fractional years 201 Installments (CI based) 190 Ratio of principal to interest 118 Population growth and depreciation 16

Simple and Compound Interest Questions

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

A man lends Rs. $12,500$ at $12$% for the first year, at $15$% for the second year and at $18$% for the third year. If the rates of interest are compounded yearly; find the difference between the C.I. for the first year and the compound interest for the third year.

  1. Rs. $1,498$
  2. Rs. $1,598$
  3. Rs. $1,298$
  4. Rs. $1,398$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
For first year
$P=12500,R=12$%, $T=1$
Interest$\cfrac { PRT }{ 100 } =1500$
Amount$=P+I=14000$
For second year previous amount will be Principle
$P=14000,R=15,T=1$
Interest'$=\cfrac { 14000\times 15\times 1 }{ 100 } =2100$
Similarly for third year
Interest''$=\cfrac { 16100\times 18\times 1 }{ 100 } =2898$
Difference between $C{ I } _{ 3 }$ & $C{ I } _{ 1 }=2898-1500=1398$
Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Mohit invests Rs. 8,000 for 3 years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs. 9,440. Calculate: the amount at the end of the second year.

  1. Rs. 15,729.50

  2. Rs. 13.079.80

  3. Rs. 12,367.50

  4. Rs. 11,139.20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$P=Rs.8000$


Amount after one year $=Rs.9440$

Interest for 1 year$=9440-8000=Rs.1440$

let rate of interest $=R$

C.I for one year=S.I for 1 year$=\dfrac{PRT}{100}$

$\Rightarrow 1440=\dfrac{8000\times R\times 1}{100}$

$\Rightarrow R=\dfrac{1440\times 100}{8000}=18$%

For second year
$P=9440$
$R=18$%
$T=1$ year

$\therefore  Amount=P\left(1+\dfrac{R}{100} \right)^T$

$\Rightarrow 9440 \left(1+\dfrac{18}{100} \right)$

$\Rightarrow 9440\times \dfrac{118}{100}=Rs.  11139.20$

Hence Amount at the end of second year $=Rs.11139.20$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Rohit lends Rs. $50,000$ at C.I. for $3$ years. If the rate of interest for the first two years is $15$% per year and for the third year it is $16$%, calculate the sum Rohit will get at the end of the third year.

  1. Rs.$77705$
  2. Rs.$76705$
  3. Rs.$74705$
  4. Rs.$78705$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  Here, $P=$Rs.$50,000,\,R _1=15\%$ and $R _2=16\%$


$\Rightarrow$  $A=P\times (1+\dfrac{R _1}{100})^2\times (1+\dfrac{R _2}{100})^1$


$\Rightarrow$  $A=50000\times (1+\dfrac{15}{100})^2\times (1+\dfrac{16}{100})^1$

$\Rightarrow$  $A=50000\times (\dfrac{23}{20})^2\times (\dfrac{29}{25})^1$

$\Rightarrow$  $A=$Rs.$76,705.$


Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Find the sum that will amount to Rs. $4,928$ in $2$ years at compound interest, if the rates for the successive years are $10$ per cent and $12$ per cent respectively.

  1. Rs. $3000$
  2. Rs. $4000$
  3. Rs. $5000$
  4. Rs. $6000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the sum be x 

Amount after 2 year=Rs.4928
Rate=10% and 12%
Time=2 years
$Amount=P\left(1+\frac{R}{100}\right)^t$
$\Rightarrow 4928=x(1+\frac{10}{100})(1+\frac{12}{100})$
$\Rightarrow 4928=x\times \frac{110}{100}\times \frac{112}{100}$
$\Rightarrow x=\frac{4928\times 100\times 100}{110\times 112}=Rs.4000$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

What principal will amount to Rs. $9,744$ in two years, if the rates of interest for successive years are $16$% and $20$% respectively?

  1. $5000$
  2. $6000$
  3. $7000$
  4. $8000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  Here $A=Rs.9744,\,T=2\,years,\,R _1=16\%$ and $R _2=20\%$

$\Rightarrow$  $A=P\times (1+\dfrac{R _1}{100})\times (1+\dfrac{R _2}{100})$

$\Rightarrow$  $9744=P\times (1+\dfrac{16}{100})\times (1+\dfrac{20}{100})$

$\Rightarrow$  $9744=P\times \dfrac{29}{25}\times \dfrac{6}{5}$

$\therefore$    $P=9744\times \dfrac{25}{29}\times \dfrac{5}{6}$

$\therefore$   $P=Rs.7000$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

What principal will amount to Rs. $38,976$ in two years, if the rates of interest for successive years are $16$% and $20$% respectively?

  1. $27000$
  2. $28000$
  3. $29000$
  4. $30000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$A=P(1+\cfrac{r}{100})^n$
for $r=16$ and $n=1$
$A=P(1+\cfrac{16}{100})^1$
$A=1.16P$
Again for $r=20, n=1,P'=1.16P$
$A=P'(1+\cfrac{r}{100})^n$
$A=1.16P\times 1.2=1.392P\\ A=Rs.38976=1.392P\\ \implies P=28000 $

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Calculate the amount and the compound interest on  $5000$ in $2$ years when the rate of interest for successive years is $6\%$ and $8\%$ respectively.

  1. $724$
  2. $727$
  3. $317$
  4. $239$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interest for the $1^{ st }$ year $=Rs$ $\cfrac { 5000\times 1\times 6 }{ 100 } =Rs$ $300$

Amount after $1^{ st }$ year $=Rs$ $5000+Rs$ $300=Rs$ $5300$
Interest for the $2^{ nd }$ year $=Rs$ $\cfrac { 5300\times 1\times 8 }{ 100 } =Rs$ $424$
Amount after $2^{ nd }$ year $=Rs$ $5300+Rs$ $424=Rs$ $5724$
$\therefore$ Compound Interest $=Rs$ $5724-Rs$ $5000= Rs$ $724$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Prem lends Rs. $100,000$ at C.I. for $3$ years. If the rate of interest for the first two years is $15$% per year and for the third year it is $16$%, calculate the sum Rohit will get at the end of the third year.

  1. Rs.$155410$
  2. Rs.$153410$
  3. Rs.$125410$
  4. Rs.$135410$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  $P=Rs.100,000,$ $R _1=15\%$ and $R _2=16\%$

$\Rightarrow$  $A=P\times (1+\dfrac{R _1}{100})^2\times (1+\dfrac{R _2}{100})^1$

$\Rightarrow$  $A=100000\times (1+\dfrac{15}{100})^2\times (1+\dfrac{16}{100})^1$

$\Rightarrow$  $A=100000\times (\dfrac{23}{20})^2\times \dfrac{29}{25}$

$\Rightarrow$  $A=100000\times \dfrac{529}{400}\times \dfrac{29}{25}$

$\Rightarrow$  $A=10\times 529\times 29$

$\therefore$    $A=Rs.153410$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Calculate the amount and the compound interest on  $17000$ in $3$ years when the rate of interest for successive years is $10\%, 10\%$ and $14\%$ respectively.

  1. $6578.70$<span class="MathJax"><span class="MJX_Assistive_MathML">6449.80$
  2. $1700$
  3. $5489.8$
  4. $6449.80$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interest for the $1^{ st } $year $=Rs$ $\cfrac { 17000\times 10\times 1 }{ 100 } =Rs$ $1700$ 

Amount after $1^{ st }$ year $=Rs$ $17000+Rs$ $1700=Rs$ $18700$
Interest for the $2^{ nd }$ year $=Rs$ $\cfrac { 18700\times 10\times 1 }{ 100 } =Rs$ $1870$ 

Amount after $2^{ nd }$ year $=Rs$ $18700+Rs$ $1870=Rs$ $20570$
Interest for the$3^{ rd }$ year $=Rs$ $\cfrac { 20570\times 14\times 1 }{ 100 } =Rs$ $2879.80$ 

Amount after $3^{ rd }$ year $=Rs$ $20570+Rs$ $2879.80=Rs$ $23449.8$
$\therefore$ Compound Interest $=Rs$ $23449.8-Rs$ $17000= Rs$ $6449.80$

Multiple choice maths banking and taxation types of accounts banks introduction, recurring deposit accounts and calculation of interest on a fixed deposit account

Ajit opens a bank account by depositing Rs $20,000$. At the end of each year, he withdraws a sum of money that makes the balance exactly half of what it was in the beginning of the year. If the bank pays $10\%$ interest, what is the total amount withdrawn by Ajit at the end of three years?

  1. Rs $17,856$
  2. Rs $20,377$
  3. Rs $18,330$
  4. Rs $19,400$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$Depositing\quad amount=Rs20000,\ Amount\quad after\quad 1\quad year=1.1*20000=Rs22000,\ Amount\quad withdrawn=amount\quad left=0.5*22000=Rs11000\ Amount\quad after\quad 2\quad year=1.1*11000=Rs12100,\ Amount\quad withdrawn=amount\quad left=0.5*12100=Rs6050\ Amount\quad after\quad 3\quad year=1.1*6050=Rs6655,\ Amount\quad withdrawn=amount\quad left=0.5*6655=Rs3327.5\ Total\quad amount\quad withdrawn=Rs3327.5+6050+11000=Rs20377.5 $

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

Choose the correct answer from the alternatives given.
Some money was lent on $4\%$ compound interest. If the difference in interest of second and the first year is $88$, find out the sum.

  1. $Rs. 50,000$
  2. $Rs. 60,000$
  3. $Rs. 65,000$
  4. $Rs. 55,000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For compound interest at rate r, the interest in the first year is P*r and in the second year is P*r*(1+r). The difference is P*r^2. Given r=0.04 and difference=88, we have P*(0.04)^2 = 88, so P*0.0016 = 88, which gives P = 55,000.

Multiple choice book keeping and accountancy bills of exchange renewal of the bill retirement and renewal of a bill accounting treatment of bill transaction

X draws a bill of exchange of Y for $Rs. 20,000$ payable in $4$ months. On the due date Y could not make the payment and requested X to renew a fresh bill for another three months at $12$% interest p.a. The amount of fresh bill will be ____________.

  1. $Rs. 20800$
  2. $Rs. 20400$
  3. $Rs. 22400$
  4. $Rs. 21300$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice book keeping and accountancy bills of exchange renewal of the bill retirement and renewal of a bill accounting treatment of bill transaction

On 1.1.05 X draws a bill on Y for Rs. 30,000 for 3 months. At maturity Y requests X accepts Rs 10,000 in cash and for balance to draw a fresh bill for 2 months together with 12% p.a interest, Amount of interest will be ___________.

  1. Rs. 400

  2. Rs. 600

  3. Rs. 480

  4. Rs. 760
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The cash paid is 10,000, leaving a balance of 20,000. Interest is charged on the balance for 2 months: 20,000 * 12% * (2/12) = 400.

Multiple choice book keeping and accountancy bills of exchange renewal of the bill retirement and renewal of a bill accounting treatment of bill transaction

On 1st Jan X draws a bill on Y for 1,50,000. At maturity Y requests X to draw a fresh bill for 2 months together with 12% p.a. interest. Nothing charges 500. The amount of interest will be:

  1. 3,000.

  2. 3,010.

  3. 2,500.

  4. 2,750.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Interest is calculated on the principal (1,50,000) plus noting charges (500) for 2 months at 12%. Interest = 1,50,500 * 0.12 * (2/12) = 3,010.