Quantitative Aptitude · Commerce Accountancy

Interest and Annuities

638 Questions

Interest and annuities represent a critical quantitative aptitude section focusing on the mathematical calculation of simple interest, compound interest, and future values of investments. Questions challenge candidates to determine maturity values, compute recurring deposit returns, and calculate prevailing interest rates. Mastery of this topic is essential for scoring high in banking and SSC examinations.

Simple and compound interestFuture value of annuitiesRecurring deposit calculationsInterest rate determinationPresent value formulas

Interest and Annuities Questions

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

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

  1. $4375$
  2. $4275$
  3. $4175$
  4. $4475$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  Here, $A=Rs.500,\, n=8$ and $r=\dfrac{8}{100}\times \dfrac{1}{4}=0.02$

$\Rightarrow$  $V=\dfrac{A}{r}\times [1-(1+r)^{-n}]$
$\Rightarrow$  $V=\dfrac{500}{0.02}\times [1-(1.02)^{-8}]$
$\Rightarrow$  Now, let $x=(1.02)^{-8}$
$\Rightarrow$  $log\,x=-8\,log\,1.02=-8(0.0086)$
$\Rightarrow$  $log\,x=-0.0688$
$\Rightarrow$  $x=0.8535$
$\Rightarrow$  $V=\dfrac{500}{0.02} \times [1-0.8535]=Rs.3662.50$
$\Rightarrow$  Now, $M=\dfrac{A}{r}\times [(1+r)^n -1]$
$\Rightarrow$  $\dfrac{500}{0.02}\times [(1.02)^8-1]$
$\Rightarrow$  Let $x=(1.02)^8$
$\Rightarrow$  $log\, x =8\, log\, (1.02)=0.0688$
$\Rightarrow$  $x=1.171$
$\therefore$   $M=\dfrac{500}{0.02}\times [1.171-1]=Rs.4275$
$\therefore$    The present value of annuity is $Rs.3662.50$ and amount is $Rs.4275$

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. $12891.50$
  2. $12610$
  3. $13861.50$
  4. $13801.50$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$   Here, $R=\left(20\times \dfrac{1}{4}\right)\%=5\%$


$\Rightarrow$   Sum borrowed = $\dfrac{4630.50}{\left(1+\dfrac{5}{100}\right)^1}+\dfrac{4630.50}{\left(1+\dfrac{5}{100}\right)^2}+\dfrac{4630.50}{\left(1+\dfrac{5}{100}\right)^3}$


$\Rightarrow$   Sum borrowed = $4630.50\times \left[\dfrac{100}{105}+\dfrac{(100)^2}{(105)^2}+\dfrac{(100)^3}{(105)^3}\right]$

$\Rightarrow$   Sum borrowed = $4630.50\times \dfrac{20}{21}\times \left[\dfrac{41}{21}+(\dfrac {20}{21})^2\right]$

$\Rightarrow$   Sum borrowed = $4410\times \dfrac{1}{21}\times \dfrac{1261}{21}=Rs.12610$

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 also the interest charged.

  1. $1281.50$
  2. $1291.50$
  3. $1181.50$
  4. $1381.50$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  Here, we have $A=Rs.4630.50,\, n=3$ and $r=\dfrac{20}{100}\times \dfrac{1}{4}=0.05$

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

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

$\Rightarrow$  $V=Rs.12610$
$\Rightarrow$  Now, Total money repaid = $3\times Rs.4630.50=Rs.13891.50$
$\therefore$   Interest paid = $Rs.13891.50-Rs.12610=Rs.1281.50$

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$
$\implies A=Rs.2920$

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 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 (approximately) with first installment.

  1. Rs. $202$
  2. Rs. $192$
  3. Rs. $92$
  4. Rs. $292$
Reveal answer Fill a bubble to check yourself
D 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$
$\implies A _1=2920(1+\cfrac{10}{100})=3212$
$CI=A _1-P=3212-2920=Rs.292$

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.