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 house is sold for $ Rs \ 30,000$ cash or $ Rs\ 17, 500$ cash down payment and instalments of $ Rs \ 1, 600$ per month for eight months. Determine the approximate rate of interest for instalment.

  1. $6.5 \%$
  2. $6 .8 \%$
  3. $ 6. 2 \%$

  4. None of these
  5. $6.3 \%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  Cash price = $Rs.30,000$

$\Rightarrow$  Cash down payment = $Rs. 17500$
$\Rightarrow$  Total amount paid in 8 monthly installments = $Rs.(1600\times 8)=Rs.12800$
$\Rightarrow$  Total amount paid under installment paln = $Rs.17500+Rs.12800=Rs.30300$
$\Rightarrow$  Interest charged = $Rs.30300-Rs.30000=Rs.300$
$\Rightarrow$  Principal for 1st month = $Rs.30000-Rs.17500=Rs.12500$
$\Rightarrow$  Principal for 2nd month = $Rs.12500-Rs.1600=Rs.10900$
$\Rightarrow$  Principal for 3rd month = $Rs.10900-Rs.1600=Rs.9300$
$\Rightarrow$  Principal for 4th month = $Rs.9300-Rs.1600=Rs.7700$
$\Rightarrow$  Principal for 5th month = $Rs.7700-Rs.1600=Rs.6100$
$\Rightarrow$  Principal for 6th month = $Rs.6100-Rs.1600=Rs.4500$
$\Rightarrow$  Principal for 7th month = $Rs.4500-Rs.1600=Rs.2900$
$\Rightarrow$  Principal for 8th month = $Rs.2900-Rs.1600=Rs.1300$
$\Rightarrow$  Total principal = $Rs.55200$
$\Rightarrow$  The last installment of Rs.1600 includes Rs.1300 plus Rs.300 interest.
$\Rightarrow$  Time = 1 month = $\dfrac{1}{12}$year, Interest = Rs.$300$
$\Rightarrow$  Interest = $\dfrac{P\times T\times R}{100}$
$\Rightarrow$  $R=\dfrac{I\times 100}{P\times T}$
$\Rightarrow$  $R=\dfrac{300\times 100}{55200\times \dfrac{1}{12}}=\dfrac{300\times 100\times 12}{55200}=\dfrac{150}{23}=6.5$
$\therefore$   $Rate =6.5\%$

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

Find the present value of an ordinary annuity of $8$ quarterly payments of Rs. $500$ each, the rate of interest being $8\%$ p.a. compounded quarterly.

  1. Rs. $3660.20$
  2. Rs. $3662.50$
  3. Rs. $4275$
  4. Rs. $3660$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $A=$ Rs $500$, $n= 8$

Also, $ r= \dfrac{8}{100} \times \dfrac{1}{4} =0.02 $

$ \therefore V= \dfrac{A}{r} \times \left[1-(1+r)^{(-n)}\right]=\dfrac{500}{0.02} \times \left[1-(1.02)^{(-8)}\right] $

Now, let $ x= (1.02)^{(-8)} $

$\Rightarrow \log{x} = -8\log{1.02}=-8(0.0086) $

$ \Rightarrow \log{x}= -0.0688 $

$ \Rightarrow x= 0.8535 $

$ \Rightarrow  V=\dfrac{500}{0.02} \times [1-0.8535] =$ Rs. $3662.50 $

Thus, the present value of annuity is Rs. $3662.50$.

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

A man borrowed some money and returned it in $3$ equal quarterly installments of Rs. $4630.50$ each. What sum did he borrow if the rate of interest was $20\%$ p.a. compounded quarterly?

  1. Rs. $12000$
  2. Rs. $12100$
  3. Rs. $12160$
  4. Rs. $13000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, we have to find present value $(V)$ of an ordinary annuity certain.

Given, $A=$ Rs. $4630.50$, $n= 3$

Also $ r= \dfrac{20}{100} \times \dfrac{1}{4}=0.05 $

$ \therefore V=\dfrac{A}{r} \times [1-(1+r)^{(-n)}] $

$=\dfrac{4630.50}{0.05} \times [1-(1.05)^{(-3)}]$

$=$ Rs. $12610 $

Thus, the sum borrowed was Rs. $12160$.

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

A man borrows Rs $37500$ and agrees to repay in semi-annual installments of Rs $2250$ each, the first due in $6$ months. How many payments must he make if rate of interest is $6\%$ compounded semi-annually?

  1. $23$
  2. $24$
  3. $25$
  4. $22$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  Here, we have to find the number of payments, $n$.

$\Rightarrow$  $V=Rs.37500$  and $A=Rs.2250$
$\Rightarrow$  Rate of interest compounded semi-annually = $\dfrac{1}{2}\times 6\% = \dfrac{1}{2}\times \dfrac{6}{100}=0.03$
$\Rightarrow$  $V=\dfrac{A}{r}\times [1-(1+r)^{-n}]$

$\Rightarrow$  $37500=\dfrac{2250}{0.03}\times [1-(1.03)^{(-n)}]$

$\Rightarrow$  $1-(1.03)^{-n}=\dfrac{37500\times 0.03}{2250}$

$\Rightarrow$  $(1.03)^{(-n)}=0.5$

$\Rightarrow$  $-n\, log(1.03)=log(0.5)$

$\Rightarrow$  $-n(0.0128)=-0.3010$

$\Rightarrow$  $n=\dfrac{-0.3010}{-0.0128}$

$\therefore$    $n=23.51 \approx 24$

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

A man borrowed some money and returned it in $3$ equal quarterly installments of Rs $4630.50$ each. Find the interest charged (in Rs) on the sum he borrowed, if the rate of interest was $20\%$ p.a. compounded quarterly?

  1. $1731.50$
  2. $1200$
  3. $1300$
  4. $1251.80$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here, we have to find present value $(V)$ of an ordinary annuity certain.

Given, $A=$ Rs $4630.50$, $n= 3$

Also $ r= \dfrac{20}{100} \times \dfrac{1}{4}=0.05 $

$ \therefore V=\dfrac{A}{r} \times [1-(1+r)^{(-n)}] =\dfrac{4630.50}{0.05} \times [1-(1.05)^{(-3)}]=$ Rs. $ \: 12610 $

Thus, the sum borrowed was Rs. $12160$

Now, total money repaid $ = 3 \times 4630.50 =$ Rs. $ \: 13891.50 $

Therefore, interest paid $ =$ Rs, $ \: 13891.50$ $-$  Rs. $ \: 12160 =$ Rs. $ \: 1731.50 $.

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

Three equal instalments each of $Rs 200$ were paid at the end of the year for the sum borrowed at $20 \%$ interest compounded annually. Find the sum. 

  1. $ 600$
  2. $421.3$
  3. $ 400$
  4. $ 431.1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Each Installment = $\dfrac{P{\cdot}r}{100[1-{\{ \dfrac{100}{100+r} \}}^n]}$
Here Installement$ = 200$
Rate of interest $(r) = 20%$
Number of years$ (n) = 3$
Solving the above equation gives $P = 421.3$

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

A sum of Rs $2500$ is invested at a rate of $5 \%$ per annum for a term of $5$ years. Find the simple interest received at the end of the term.

  1. $1250$
  2. $625$
  3. $1200$
  4. $1500$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  Here, $P=Rs.2500,\, R=5\%,\, T=5\,years$.

$\Rightarrow$  $Simple\, Interest=\dfrac{P\times R\times T}{100}$
$\Rightarrow$  $\dfrac{2500 \times 5\times 5}{100}$
$\Rightarrow$  $25\times 25$
$\therefore$  $Simple\, Interest\, =Rs.625$

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

A $5-$year ordinary annuity has a present value of $\$1,000$.  If the interest rate is $8$ percent, the amount of each annuity payment is closest to which of the following? 

    1. $ $250.44$
    2. $ $231.91$
    3. $ $181.62$
    4. $ $184.08$
    5. $ $170.44$
    Reveal answer Fill a bubble to check yourself
    A Correct answer
    Explanation

    $\Rightarrow$   We have, $V=\$1000\, r=8\%=0.08$ and $n=5$

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

    $\Rightarrow$  $A=\dfrac{1000\times 0.08}{1-(1.08)^{-5}}$

    $\therefore$     $A=\$250.44$

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

    A man borrows $Rs \ 1820$ and undertakes to payback with a compound interest of $20 \%$ per annum in a $3$  equal yearly installments at the end of first year, second year and third year. Find the amount of each installments 

    1. $864$
    2. $800$
    3. $900$
    4. $820$
    Reveal answer Fill a bubble to check yourself
    A Correct answer
    Explanation

    Each Installment = $\dfrac{P{\cdot}r}{100[1-{{ \frac{100}{100+r} }}^n]}$

    here $P = Rs1820$
    $r=0.2$
    $n=3$
    solving gives $Installment = 864Rs$

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

    An 8-year annuity due has a present value of $ $1,000$.  If the interest rate is $5$ percent,  the amount of each annuity payment is closest to which of the following? 

    1. $ $154.73$
    2. $ $147.36$
    3. $ $109.39$
    4. $ $104.72$
    5. $ $99.74$
    Reveal answer Fill a bubble to check yourself
    A Correct answer
    Explanation

    $\Rightarrow$  We have, $V=\$1000,\, n=8$ and $r=5\%=0.05$.

    $\Rightarrow$  We know, $V=\dfrac{A}{r}\times [1-(1+r)^{-n}]$
    $\Rightarrow$  $A=\dfrac{V\times r}{[1-(1+r)^{-n}]}$

    $\Rightarrow$  $A=\dfrac{1000\times 0.05}{[1-(1.05)^{-8}]}$

    $\Rightarrow$  $A=\$154.73$

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

    For son's education , a man sets aside Rs $4000$ at the end of every year for $8$ years . If the rate of interest is 15 % per annum C.I. , what is the value of his sinking fund.

    1. 54909.33

    2. 53909.33

    3. 52909.33

    4. 51909.33
    Reveal answer Fill a bubble to check yourself
    A Correct answer
    Explanation

    Using formula of sinking fund

    $M=\cfrac{A}{r}[(1+r)^n-1]$
    $\implies \cfrac{4000}{0.15}[(1+0.15)^8-1]=54907.2763\approx 54.909.83$

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

    A man borrows Rs. $ 30000$ at $12 \%$ per annum compound interest from a bank and promises to pay off the loans in $20$ annual instalments beginning at the end of the first year . What is the annual payment necessary?

    1. $4016.76$
    2. $3013.54$
    3. $4065.24$
    4. $1034.54$
    Reveal answer Fill a bubble to check yourself
    A Correct answer
    Explanation

    Here, $V=Rs.30000,\,\,r=12\%=0.12$ and $n=20$.

    We know $V=\dfrac{A}{r}[1-(1+r)^{-n}]$
    Thus $30000=\dfrac{A}{0.12}[1-(1+0.12)^{-20}]$
    $\Rightarrow$   $A=\dfrac{30000\times 0.12}{[1-(1+0.12)^{-20}]}$
    $\Rightarrow$  $A=\dfrac{3600}{[1-(1.12)^{-20}]}$
    $\Rightarrow$  $A=$ Rs. $4016.76$

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

    A person borrowed some money and returned it in 3 equal quarterly instalments of Rs 4630.50 each. What sum (approximately) did he borrow if the rate of interest was 20 % per annum.compounded quarterly?

    1. 12613.48

    2. 10613.48

    3. 11613.48

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

    $\Rightarrow$  We have $A=Rs.4630.50,\, n=3$ and rate of interest is $20\%$ which is compounded quarterly. So, $r=5\%$

    $\Rightarrow$ We have to find sum borrow i.e. $V$
    $\Rightarrow$  $V=\dfrac{A}{r}[1-(1+r)^{-n}]$

    $\Rightarrow$  $V=\dfrac{4630.50}{0.05}[1-(1+0.05)^{-3}]$  

    $\Rightarrow$  $V=\dfrac{463050}{5}[1-(1.05)^{-3}]$

    $\Rightarrow$  $V=92610\times \dfrac{1261}{9261}$

    $\Rightarrow$  $V=10\times 1261$

    $\Rightarrow$  $V=Rs.12610$

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

    A person takes a loan on compound interest and returns it in $2$ equal installments . If the rate of interest is $10$% per annum and the yearly installment is Rs $1682$. Find the interest charged with second installment.

    1. Rs.$613.2$
    2. Rs.$603.2$
    3. Rs.$513.2$
    4. Rs.$713.2$
    Reveal answer Fill a bubble to check yourself
    A Correct answer
    Explanation

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

    $\implies \cfrac{1682}{(1+\cfrac{10}{100})^1}$$+\cfrac{1682}{(1+\cfrac{10}{100})^2}$
    $ \implies 1592.09+1390.08=2919.17\approx 2920$
    $\implies A _2=2920(1+\cfrac{10}{100})^2=3533.2$
    $CI=A _1-P=3533.2-2920=Rs.613.2$

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

    A person takes a loan on compound interest and returns it in $2$ equal installments . If the rate of interest is $10$% per annum and the yearly installment is Rs $1682$. Find the principal (approximately).

    1. $2920$
    2. $3450$
    3. $2346$
    4. $2275$
    Reveal answer Fill a bubble to check yourself
    A Correct answer
    Explanation

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

    $\implies \cfrac{1682}{1+(\cfrac{10}{100})^1}$$+\cfrac{1682}{1+(\cfrac{10}{100})^2}$
    $ \implies 1592.09+1390.08=2919.17\approx 2920$
    $\implies A=Rs.2920$