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 business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

Find the future value of an annuity of Rs. $500$ made annually for $7$ years at interest rate of $14\%$ compounded annually. Given that $(1.14)^7=2.5023$.

  1. $5,563.25$
  2. $5,365.35$
  3. $5,365.53$
  4. $5,356.35$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Annual payment A$=$Rs. $500$
$n=7$
$i=14\%=0.14$
$A(7, 0.14)=500\left[\displaystyle\frac{(1+1.014)^7-1}{0.14}\right]$
$=$Rs. $5365.35$

Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

A limited company intends to create a depreciation fund to replace at the end of the 25th year assets costing Rs 100000.Calculate the amount (approximately) to be retained out of profits every year if the interest rate is 3%.

  1. 2755

  2. 3245

  3. 5431

  4. 1200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a sinking fund calculation to reach a future value of 100,000 in 25 years at 3% interest. Using the formula PMT = FV * i / ((1+i)^n - 1), the result is approximately 2755.

Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

An investor deposits Rs 1000 in a saving institution. Each payment is made at the end of year.If the payment deposited earns 12% interest compounded annually how much amount(approximately) will he receive at the end of 10 years.

  1. $1234$
  2. $2345$
  3. $17548$
  4. $4567$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$P=Rs.1000,r=12\%,t=10$

$A=\sum _{ n=1 }^{ 9 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n }+P } \ =\sum _{ n=1 }^{ 9 }{ 1000{ (1+\cfrac { 12 }{ 100 } ) }^{ n }+1000 } \ =3000\times 16.548\ =Rs.17548$

Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

A man decides to deposit Rs 3000 at the end of each year in a bank which pays 3% p.a compound interest . If the instalments are allowed to accumulate , what will be the total accumulation at the end of 15 years.

  1. Rs.$57450$
  2. Rs.$67780$
  3. Rs.$67050$
  4. Rs.$98450$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=Rs.3000,r=3\%,t=15$
$A=\sum _{ n=1 }^{ 15 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n } } \ =\sum _{ n=1 }^{ 15 }{ 3000{ (1+\cfrac { 3 }{ 100 } ) }^{ n } } \ =3000\times 19.15\ =Rs.57450$

Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

A company borrows Rs 10000 on condition to repay it with compound interest at $5$% p.a . by annual instalments at Rs 1000 each. In how many years will the debt be paid off?

  1. 14.2

  2. 21.7

  3. 12.67

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\Rightarrow$  Company borrow Rs.10000 i.e. $pv=Rs.10000$ and $I=5\%=0.05$. $A$ is also given which is $Rs.1000$
$\Rightarrow$  Present value of annuity regular
$\Rightarrow$  $pv=A\times [\dfrac{(1+I)^n-1}{I\times (1+I)^n}]$

$\Rightarrow$  $10000=1000\times [\dfrac{(1+0.05)^n-1}{0.05\times (1+0.05)^n}]$

$\Rightarrow$  $(1.05)^n-0.5\times (0.5)^n=1$
$\Rightarrow$  $(1.05)^n=2$
Taking log both sides
$\Rightarrow$  $n=\dfrac{log\,2}{log\, 1.05}$
$\therefore$   $n=14.2\, years$
Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

Mr Dev purchased a car paying Rs $90,000$ and promising to pay Rs 5000 every 3 months for the next 10 years. The interest is $6$% p.a. compounded quarterly. If at the end of 5th year , he wants to finish his liability by a single payment , how much should he pay?

  1. 90100

  2. 80100

  3. 34504

  4. 54345
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have $A=Rs.5000,\,I=\dfrac{6}{100}\times \dfrac{1}{4}=0.015$ and $n = 20$

$\Rightarrow$  If at the end of 5th year, i.e., at the time of 20th payment, he wants to finish off the liability, then lump sum payment required is,
$\Rightarrow$  $5000$ + Present value of the remaining 20 installments.
$\Rightarrow$  $5000+V$
$\Rightarrow$  $5000$ + $\dfrac{A}{I}[1-(1+I)^{-n}]$

$\Rightarrow$  $5000+\dfrac{5000}{0.015}[1-(0.015)^{-20}]$    ---- ( 1 )

$\Rightarrow$  Let $x=(1.015)^{-20}$
$\Rightarrow$  $log\,x=-20\,log\,(1.015)$
$\Rightarrow$  $log\,x=-20(0.0064)=-0.128=\bar{1}.8720$
$\Rightarrow$  $x=antilog\,(\bar{1}.8720)=0.7447$
Substitute value of $x$ in ( 1 ),
$\Rightarrow$  $5000+\dfrac{5000}{0.015}(1-0.7447)$

$\Rightarrow$  $5000+\dfrac{5000}{0.015}\times 0.2553$

$\Rightarrow$  $Rs.90100$

Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

Amit buys a house for Rs 500000. The contract is that amit will pay Rs 200000 immediately and the balance in 15 equal instalments with 15 % p.a compound interest . How much has he to pay annually (approximately)?

  1. Rs$51,305$
  2. Rs$54,005$
  3. Rs$51,843$
  4. Rs$91,305$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Present value $=Rs.50,000Rs.20,000=Rs.30,000$

$P=\cfrac{A}{(1+\cfrac{R}{100})^n}$

$\implies 30,000=\cfrac{A}{1+(\cfrac{15}{100})}$$+\cfrac{A}{1+(\cfrac{15}{100})^2}+.....$4
$ \implies A\times 5,847 $

$\implies A=Rs51,305$

Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

Z invests Rs. $10,000$ every year starting for today for next $10$ years. Suppose interest rate is $8\%$ per annum compounded annually. Calculate future value of the annuity. Given that $(1+0.08)^{10}=2.15892500$.

  1. $1,44,865.625$
  2. $1,56,454.875$
  3. $1,54,654.875$
  4. $1,44,568.625$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Step-$1$: Calculate future value as though it is an ordinary annuity
Future value of the annuity as if it is an ordinary annuity
$=10,000\left[\displaystyle\frac{(1+0.08)^{10}-1}{0.08}\right]$
$=10,000\times 14.4865625$
$=Rs. 1,44,865.625$
Step-$2$: Multiply the result by $(1+i)$
$=1,44,865.625\times (1+0.08)$
$=1,56454.875$.

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

If the interest on $1700$ rupees is $340$ rupees for $2$ year the rate of interest must be

  1. $12\ \%$
  2. $15\ \%$
  3. $4\ \%$
  4. $10\ \%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Principle$=Rs1770\quad\quad Time=2years$

$SI=Rs340\quad\quad Rate=?\ \cfrac{P\times R\times T}{100}=340\Rightarrow \cfrac{1770\times R\times 2}{100}=340\ \Rightarrow R=\cfrac{340\times100}{1770\times2}=\cfrac{340\times5}{177}=9.6\%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

The simple interest on a sum money is 4/9 of the principal and the number of years is equal to the rate percent per annum. The rate per annum is :  

  1. $5$%
  2. $6\dfrac{2}{3}\%$
  3. $6$%
  4. $7\dfrac{1}{5}\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let the principal be $P$.
Rate of interest be $R\%$
According to the question, Time$=R$
Simple interest $=\dfrac{4P}{9}$.
$SI =\dfrac{\left(PTR\right)}{100}$
$\Rightarrow \dfrac{4P}{9} =\dfrac{\left(PTR\right)}{100}$
$\Rightarrow \dfrac{4P}{9} =\dfrac{\left(P\times R\times R\right)}{100}$
$\Rightarrow \dfrac{4P}{9} =\dfrac{\left(P\times {R}^{2}\right)}{100}$
$\Rightarrow \dfrac{4}{9} =\dfrac{{R}^{2}}{100}$
$\Rightarrow {R}^{2}=100\times\dfrac{4}{9}$
$\Rightarrow R= 10\times \dfrac{2}{3}=\dfrac{20}{3}$
Therefore, rate of interest is $\dfrac{20}{3}\%$ or  $6\dfrac{2}{3}\%$.

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate per cent per annum, will Rs.32000 yield a compound interest of Rs.5044 in 9 months interest being compounded quarterly ?

  1. 25

  2. 23

  3. 20

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Principal = Rs.32000 
Amount $= Rs.(32000 + 5044) = Rs.37044$
Rate $= r\%$ p.a. or $\displaystyle \cfrac{r}{4}\%$ per quarter 
Time = 9 months = 3 quarters i.e., $n = 3$
$\displaystyle \therefore$ Applying $\displaystyle A=P\left ( 1+\cfrac{r}{100} \right )^{n}$ we have
$\displaystyle 37044=32000\left ( 1+\cfrac{r}{400} \right )^{3}\Rightarrow \cfrac{37044}{32000}=\left ( 1+\cfrac{r}{400} \right )^{3}$
$\displaystyle \Rightarrow \cfrac{9261}{8000}=\left ( 1+\cfrac{r}{400} \right )^{3}\Rightarrow \left ( \cfrac{21}{20} \right )^{3}=\left ( 1+\cfrac{r}{400} \right )^{3}$
$\displaystyle \Rightarrow 1+\cfrac{r}{400}=\cfrac{21}{20}\Rightarrow \cfrac{r}{400}=\cfrac{21}{20}-1=\cfrac{1}{20}\Rightarrow r=\cfrac{400}{20}=20\%p.a.$
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate of interest per annum will a sum double itself in 8 years?

  1. $25\%$
  2. $6\frac{1}{4} \%$
  3. $12\frac{1}{2} \%$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

T = 8 years; N = 2; R = ?
R $\times T$ = 100 $\times (N - 1)$


R $\times 8$= 100 $\times (2 - 1)$

$R\, =\, \displaystyle \frac {100}{8}\, =\, 12\frac{1}{2}\, \%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

Simple interest on Rs.2000 for 4 years is Rs.400. Percent rate of interest is

  1. $\displaystyle\frac{2000\times 100}{400\times 4}$
  2. $\displaystyle\frac{400\times 4}{2000\times 100}$
  3. $\displaystyle\frac{400\times 100}{2000\times 4}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Principal = Rs 2000
Time = 4 years
Interest = Rs 400
Now, $Interest = \frac{Principal \times Rate \times Time}{100}$
$400 = \frac{2000\times R\times 4}{100}$
$R = \frac{400 \times 100}{2000 \times 4}$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years?

  1. $4\frac {1}{2}$%
  2. $5\frac {1}{2}$%

  3. 4%

  4. 5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$SI=\frac {2}{5}P, t=10, r=?$
$\frac {Ptr}{100}=\frac {2}{5}P$
or $\frac {10\times r}{100}=\frac {2}{5}$
or $r=\frac {20}{5}=4$%

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A person finds that an increase in the rate of interest from $\displaystyle4\frac{7}{8}$% to $\displaystyle5\frac{1}{8}$% per annum increases his yearly income by Rs 30. His capital in rupees is

  1. 15,000

  2. 14,000

  3. 13,000

  4. 12,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

increase in rate of interest

$4\frac { 7 }{ 8 } =\frac { 39 }{ 8 } $
$5\frac { 1 }{ 8 } =\frac { 41 }{ 8 } $
$\frac { 41 }{ 8 } -\frac { 39 }{ 8 } =\frac { 2 }{ 8 } $
$\frac { 2 }{ 8 } $% of income is Rs30 of the capital
$1$% of income is $\frac { 8 }{ 2 } \times 30$ of capital
$100$% of income will be$\frac { 8 }{ 2 } \times 30\times 100=12000$
His capital in rupees is 12000