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

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 future value of an ordinary amount of Rs 4000 each six months for 10 years at 8% per annum , compounded semi-annually.

  1. $123877$
  2. $175640$
  3. $213457$
  4. $324156$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=Rs.4000$

Amount payable in half yearly so $,r=8\%/2=4\%,t=10\times 2=20$
$A=\sum _{ n=1 }^{ 20 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n } } \ =\sum _{ n=1 }^{ 20 }{ 4000{ (1+\cfrac { 4 }{ 100 } ) }^{ n } } \ =4000\times 30.969\ =Rs.123877$

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

Find the least number of years for which an annuity Rs 1000 must run in order that its amount just exceeds Rs 16000 at 5% pa. compounded annually.

  1. $12$
  2. $9$
  3. $2$
  4. $25$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=4000, r=5\%$

$A=\sum _{ n=1 }^{ n _0 }{ P{ (1+\cfrac { r }{ 100 } ) }^{ n } } \ =\sum _{ n=1 }^{ n _0 }{ 1000{ (1+\cfrac { 5 }{ 100 } ) }^{ n }\  } >1600\ =\sum _{ n=1 }^{ n _0 }{ { (1+\cfrac { 5 }{ 100 } ) }^{ n }\  } >16$
Since it is a sum of a infinite GP. We can write it as a
$\cfrac  {(1.05^{n _0}-1)}{(1.05-1)}\times 1.05>16$
$\implies (1.05)^{n _0}>1.7619$
Taking log on both sides
$\implies \log{(1.05)^{n _0}}>\log 1.7619$
$\implies n _0>\cfrac{\log (1.7619)}{\log (1.05)}$
$\implies n _0>11.6$
$\implies n _0=12$
Hence, least no. of years$=12$.

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

A sum of Rs 2522 is borrowed from a money lender at 5% per annum compounded annually.If this amount is to be paid back in 3 equal instalments , find the annual instalments (approximately).

  1. 925

  2. 800

  3. 875

  4. 567
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

$\implies 2522= \cfrac{A}{(1+\cfrac{5}{100})^1}$$+\cfrac{A}{(1+\cfrac{5}{100})^2}+$$\cfrac{A}{(1+\cfrac{5}{100})^3}$
$ \implies A=926\approx 925$

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

The present value of an annuity of Rs. $3,000$ for $15$ years at $4.5\%$ p.a. CI is?

  1. Rs. $23,809.41$
  2. Rs. $32,218.63$
  3. Rs. $32,908.41$

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

Payment $P=3000$

$n=15$ years
rate=$4.5%$
$\therefore r=\cfrac { 4.5 }{ 100 } \ =0.045\ PV=P\left( \cfrac { 1-(1+r)^{ -n } }{ r }  \right) \ =3000(\cfrac { 1-(1+(1+0.045)^{ -15 } }{ 0.045 } )\ =3000(\cfrac { 1-(1.045)^{ -15 } }{ 0.045 } )\ =32218.63$
 $\therefore PV$ of the annuity is 
 $32218.63.$

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. $2,044$.