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

A sinking fund is created for the redemption of debentures of Rs 10,000 at the end of 25 years. How much money should be provided out of profits each year for the sinking fund if the investment can earn interest at the rate 4% per annum?

  1. 2408.19

  2. 1408.19

  3. 3408.19

  4. 5408.19
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using formula of sinking fund

$M=\cfrac{A}{r}[(1+r)^n-1]$
$\implies 1000= \cfrac{A}{0.04}[(1+0.04)^{25}-1]\implies A=2408.19$

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

A man borrowed some money and paid back in 3 equal instalments of Rs 2160 each. What sum did he borrow if the rate of interest charged was 20 % p.a .compounded annually?

  1. 4551.12

  2. 4334.24

  3. 4768.97

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

We know that,

$A=P(1+\cfrac{r}{100})^n$
$\implies 2160=P(1+\cfrac{20}{100})^2\ \implies P=Rs.4551.12$

Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics
A man borrowed some money and paid back in $3$ equal instalments of Rs. $2160$ each. The rate of interest charged was $20\%$ p.a .compounded annually. Find the total interest charged in Rs.(approximately).
  1. $1928$
  2. $1980$
  3. $1930$
  4. $1954$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  We have, $A=Rs.2,160,\, n=3\, and\, r=20\%$

$\Rightarrow$  First we have to find Sum borrowed i.e. $V$.
$\Rightarrow$  Using, $V=\dfrac{A}{r}[1-(1+r)^{-n}]$


$\Rightarrow$  $V=\dfrac{2160}{0.2}[1-(1.2)^{-3}]$

$\Rightarrow$  $V=10800[1- \dfrac{1000}{(12)^3}]$

$\Rightarrow$  $V=10800[\dfrac{(1728-1000)}{1728}]$

$\Rightarrow$  $V=\dfrac{10800\times 728}{1728}$

$\Rightarrow$  $V=Rs.4550$.
$\Rightarrow$  Total interest = $(A\times n)-V=2160\times 3-4550=Rs. 1930$

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. What is the cash value (approximately) of the car ?

  1. 238467

  2. 235467

  3. 228467

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

$\Rightarrow$  We have, $A=Rs.5000,\, n=40$ and $I=\dfrac{6}{100}\times \dfrac{1}{4}=0.015$

$\Rightarrow$  $V=\dfrac{A}{I}[1-(1+I)^{-n}]$

$\Rightarrow$  $V=\dfrac{5000}{0.015}[1-(1+0.015)^{-40}]$      ---   ( 1 )

$\Rightarrow$  Let $x=(1.015)^{-40}$
$\Rightarrow$  $log\, x=-40(0.0064)$
$\Rightarrow$  $log\, x=-0.256=(\bar{1}.7440)$
$\Rightarrow$   $x=antilog (\bar{1}.7440)$
$\Rightarrow$   $x=0.5546$
     Substitute this value in ( 1 ),
$\Rightarrow$  $V=\dfrac{5000}{0.015}(1-0.5546)$

$\Rightarrow$  $V=\dfrac{5000}{0.015}\times 0.4454=Rs.148466.67$

$\therefore$   Total cash value of the car = $Rs.90000+Rs.148466.67$
$\Rightarrow$  Total cash value of car = $Rs.2,38,467$ approx.

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

Find the amount(approximately) of an annuity immediate of Rs 2000 per annum for 20 years. The rate of interest is $\dfrac{27}{2}$ % per annum.

  1. 171703

  2. 19000

  3. 21345

  4. 43251
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$n=20,r=(27/2)\%,P=Rs.2000$
$A=P(1+\cfrac{r}{100})^n$
$\implies A=2000[(1+\cfrac{(27/2)}{100})^{20}$$+(1+\cfrac{(27/2)}{100})^{19}......$$+(1+\cfrac{(27/2)}{100})^{1}]\\A=2000\times 85.85\\ A=Rs.171700\approx 171703$

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

Mr Assem decides to deposit Rs 5000 at the end of year in a bank which pays compound interest the rate of 5% per annum. What will be his total accumulation (approximately) at the end of 15 years?

  1. Rs.$140092$
  2. Rs.$907892$
  3. Rs.$100892$
  4. Rs.$107892$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$A=P(1+\cfrac{r}{100})^n$
$\implies A=5000[(1+\cfrac{5}{100})$$+(1+\cfrac{5}{100})^{14}......$$+(1+\cfrac{5}{100})^{1}+5000]\\=5000\times 21.5718\\ Rs.107892$
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 promised to pay Rs 5000 every 3 months for the next 10 years. The interest is $6$% p.a. compounded quarterly. If Mr Dev misses first 6 payments , how much should he pay at the time of 7th payment (approximately) to bring himself up to date.

  1. 36333

  2. 46532

  3. 56734

  4. 60322
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have $A=Rs.5000,\, n=7$  $I=\dfrac{6}{100}\times \dfrac{1}{4}=0.015$

$\Rightarrow$  At the time of 7th payment, equivalent amount of first 6 missed payment has also to be paid. Thus total payment to be made at the end of 7th period is the amount of annuity of 7 terms. Hence, amount required required to be paid is,
$\Rightarrow$  $M=\dfrac{A}{I}[(1+I)^{n}-1]$


$\Rightarrow$  $M=\dfrac{5000}{0.015}[(1.015)^{7}-1]$           -----  ( 1 )
$\Rightarrow$   Let $x=(1.015)^{7}$
$\Rightarrow$   $log\,x=7\,log\,(1.015)$
$\Rightarrow$   $log\,x=7\,(0.0064)=0.0448$
$\Rightarrow$   $x=antilog\,(0.0448)$
$\Rightarrow$   $x=1.109$
Substitute value of $x$ in ( 1 ) we get,
$\Rightarrow$  $M=\dfrac{5000}{0.015}(1.109-1)$

$\Rightarrow$  $M=\dfrac{5000}{0.015}\times 0.109$

$\Rightarrow$  $M=\dfrac{5000\times 1000}{15}\times \dfrac{109}{1000}$

$\Rightarrow$  $M=Rs.36333.33\approx Rs.36333$

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

A bank pays interest at the rate of 8 % per annum compounded half yearly. Find how much should be deposited in the bank (approximately) at the beginning of each half year in order to accumulate Rs 8000 for 3 years.

  1. 994

  2. 1161

  3. 4532

  4. 2341
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$A=P(1+\cfrac{r}{100})^n$
$r=8\%/2=4\%, n=2\times 3=6$
$\implies 8000=P[(1+\cfrac{4}{100})^6$$+(1+\cfrac{4}{100})^{5}......$$+(1+\cfrac{4}{100})^{1}]\\ \implies 8000=P\times 21.5718\\ \implies P=Rs.1159\approx Rs.1161$

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

Find the amount of the annuity of Rs 150 payable in half yearly instalments  for 15 years at 4% per annum interest also payable half yearly

  1. Rs.$9903.45$
  2. Rs.$3003.45$
  3. Rs.$8103.45$
  4. Rs.$3103.45$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$P=Rs.150$

Amount payable in half yearly so $,r=4\%/2=2\%,t=15\times 2=30$
$A=\cfrac{1}{2}\sum _{ n=1 }^{ 30 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n } } \ =\cfrac{1}{2}\sum _{ n=1 }^{ 30 }{ 150{ (1+\cfrac { 2 }{ 100 } ) }^{ n } } \ =75\times 41.38\ =Rs.3103.45$

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

What is the amount of annuity(approximately) due of Rs 100 yearly payable half yearly for 15 years at 10 % compound interest per annum half yearly.

  1. 3491

  2. 1456

  3. 5434

  4. 2341
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$r=\cfrac{10\%}{2}=5\%,n=2\times 15=30,A=Rs.100$

Amount of annuity due payable half yearly
$=(1/2)\cfrac{A}{r}\times (1+r)\times[(1+r)^n-1]$
$=(1/2)\cfrac{100}{0.05}\times (1+0.05)\times[(1+0.05)^{30}-1]\=Rs.3488\approx  Rs.3491$

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

Suppose you deposit $ \$900$ per month into an account that pays $4.8 \%$ interest, compounded monthly. How much money will you have after $9$ months? 

  1. $ $8432.97$
  2. $ $1372.44$
  3. $ $9812.97$

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

Here, $P=\$900,\,R=4.8\%$ and $T=9$ months $=\dfrac{3}{4}$ year

$\Rightarrow$ $A=P\left (1+\dfrac{R}{100}\right)^{4T}$
$\Rightarrow$ $A=900\times \left (1+\dfrac{4.8}{100}\right)^{4\times \frac{3}{4}}$
$\Rightarrow$ $A=900\times \left (\dfrac{131}{125}\right)^3=900\times 1.1510$
$\Rightarrow$ $A=\$1035.9$

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

What amount should be set aside at the end of each year to amount Rs 10 lakhs at the end of 15 years at 6% per annum compound interest?

  1. $5298994$
  2. $3297000$
  3. $4297994$

  4. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$A=10,00,000, t=15,r=6\%$

$A=\sum _{ n=1 }^{ 14 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n }+P } $
$\implies 10,00,000=P[\sum _{ n=1 }^{ 14 }{ { (1+\cfrac { 6 }{ 100 } ) }^{ n }+ 1} ]$
$\implies 10,00,000\times (22.276+1)\ \implies P=Rs.42963$

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

Find the amount of annuity of Rs. 4,000 per annum for 10 years reckoning interest at 10% p.a.
[Given : $(1.1)^{10} = 2.594$]

  1. Rs. 63,760

  2. Rs. 63,670

  3. Rs. 63,205

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

$P=Rs.4000$

$n=10$
$x=10$%
    $=\dfrac { 10 }{ 100 } =0.1$
$M=\dfrac { P }{ r } \left( { \left( 1+r \right)  }^{ n }-1 \right) $
     $=\dfrac { 4000 }{ 0.1 } \left( { \left( 1.1 \right)  }^{ 10 }-1 \right) $
     $=40000(2.594-1)$
     $=63760$.
$\therefore $  Amount of annuity $=63760$

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

Rs. $200$ is invested at the end of each month in an account paying interest $6\%$ per year compounded monthly. What is the future value of this annuity after $10$th payment? Given that $(1.005)^{10}=1.0511$.

  1. $2,044$
  2. $2,404$
  3. $2,440$
  4. $2,004$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A$=$Rs. $200$
$n=10$
i$=6\%$ p.a. $=6/12\%$ per month $=0.005$
Future value of annuity after $10$ months is given by
A(n, i)$=A\left[\displaystyle\frac{(1+i)^n-1}{i}\right]$
$A(10, 0.005)=200\left[\displaystyle\frac{(1+0.005)^{10}-1}{0.005}\right]$
$=$Rs. $2,044$.