Quantitative Aptitude · Commerce Accountancy

Interest and Annuities

621 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

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.

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$