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 mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Rohit lends Rs. $50,000$ at C.I. for $3$ years. If the rate of interest for the first two years is $15$% per year and for the third year it is $16$%, calculate the sum Rohit will get at the end of the third year.

  1. Rs.$77705$
  2. Rs.$76705$
  3. Rs.$74705$
  4. Rs.$78705$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  Here, $P=$Rs.$50,000,\,R _1=15\%$ and $R _2=16\%$


$\Rightarrow$  $A=P\times (1+\dfrac{R _1}{100})^2\times (1+\dfrac{R _2}{100})^1$


$\Rightarrow$  $A=50000\times (1+\dfrac{15}{100})^2\times (1+\dfrac{16}{100})^1$

$\Rightarrow$  $A=50000\times (\dfrac{23}{20})^2\times (\dfrac{29}{25})^1$

$\Rightarrow$  $A=$Rs.$76,705.$


Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Mohit invests Rs. 8,000 for 3 years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs. 9,440. Calculate: the interest accured in the third year.

  1. Rs. 2,005.06

  2. Rs. 2,196.06

  3. Rs. 2,207.06

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

$P=Rs.8000$


Amount after one year $=Rs.9440$

Interest for 1 year$=9440-8000=Rs.1440$

let rate of interest=R

C.I for one year=S.I for 1 year$=\dfrac{PRT}{100}$

$\Rightarrow 1440=\dfrac{8000\times R\times 1}{100}$

$\Rightarrow R=\dfrac{1440\times 100}{8000}=18$%

For second year
$P=9440$
$R=18$ %
$T=1$ year

$\therefore  Amount=P \left(1+\dfrac{R}{100} \right)^T$

$\Rightarrow 9440 \left(1+\dfrac{18}{100} \right)$

$\Rightarrow 9440\times \dfrac{118}{100}=Rs.  11139.20$

Hence Amount at the end of second year $=Rs.11139.20$

For the third year
$P=Rs.11139.20$
$R=18$%
$T=1$ year

$Interest=\dfrac{11139.20\times 18\times 1}{100}=Rs. 2005.06$

Hence interest for third year $=Rs.2005.06$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Find the sum that will amount to Rs. $4,928$ in $2$ years at compound interest, if the rates for the successive years are $10$ per cent and $12$ per cent respectively.

  1. Rs. $3000$
  2. Rs. $4000$
  3. Rs. $5000$
  4. Rs. $6000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the sum be x 

Amount after 2 year=Rs.4928
Rate=10% and 12%
Time=2 years
$Amount=P\left(1+\frac{R}{100}\right)^t$
$\Rightarrow 4928=x(1+\frac{10}{100})(1+\frac{12}{100})$
$\Rightarrow 4928=x\times \frac{110}{100}\times \frac{112}{100}$
$\Rightarrow x=\frac{4928\times 100\times 100}{110\times 112}=Rs.4000$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

What sum will amount to Rs. $659340$ in $2$ years C.I., if the rates are $10$ per cent and $11$ per cent for the successive years?

  1. $540000$
  2. $550000$
  3. $560000$
  4. $570000$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$   Here, $A=Rs.659340,\,R _1=10\%,\,R _2=11\%$

$\Rightarrow$   $A=P(1+\dfrac{R _1}{100})^T\times (1+\dfrac{R _2}{100})^T$

$\Rightarrow$  $659340=P\times (1+\dfrac{10}{100})^1\times (1+\dfrac{11}{100})^1$

$\Rightarrow$  $659340=P\times \dfrac{11}{10}\times \dfrac{111}{100}$

$\Rightarrow$  $659340=P\times \dfrac{1221}{1000}$

$\Rightarrow$  $P=540\times 1000$

$\therefore$    $P=Rs.540000.$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

What principal will amount to Rs. $9,744$ in two years, if the rates of interest for successive years are $16$% and $20$% respectively?

  1. $5000$
  2. $6000$
  3. $7000$
  4. $8000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  Here $A=Rs.9744,\,T=2\,years,\,R _1=16\%$ and $R _2=20\%$

$\Rightarrow$  $A=P\times (1+\dfrac{R _1}{100})\times (1+\dfrac{R _2}{100})$

$\Rightarrow$  $9744=P\times (1+\dfrac{16}{100})\times (1+\dfrac{20}{100})$

$\Rightarrow$  $9744=P\times \dfrac{29}{25}\times \dfrac{6}{5}$

$\therefore$    $P=9744\times \dfrac{25}{29}\times \dfrac{5}{6}$

$\therefore$   $P=Rs.7000$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Vaibhav lent out Rs.$70,000$ at $6$% and Rs.$95,000$ at $5$%. Find his total income from the interest in 3 years.

  1. $26850$
  2. $25650$
  3. $25950$
  4. $26000$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here $P=Rs.70000,\,T=3\,years$ and $R=6\%$

$\Rightarrow$  $S.I.=\dfrac{P\times R\times T}{100}$

$\Rightarrow$  $S.I.=\dfrac{70000\times 6\times 3}{100}=Rs.12,600$

$\Rightarrow$  Now, $P=Rs.95000,\,T=3\,years$ $R=5\%$

$\Rightarrow$  $S.I.=\dfrac{P\times R\times T}{100}=\dfrac{95000\times 5\times 3}{100}$

$\Rightarrow$  $S.I.=Rs.14,250$.

$\therefore$   Total earning from investment = $Rs.12,600+Rs.14,250=Rs.26,850$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

What sum will amount to Rs. $65934$ in $2$ years C.I., if the rates are $10$ per cent and $11$ per cent for the successive years?

  1. $54000$
  2. $55000$
  3. $56000$
  4. $57000$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$   Here, $A=Rs.65934,\,R _1=10\%,\,R _2=11\%$

$\Rightarrow$   $A=P(1+\dfrac{R _1}{100})^T\times (1+\dfrac{R _2}{100})^T$

$\Rightarrow$  $65934=P\times (1+\dfrac{10}{100})^1\times (1+\dfrac{11}{100})^1$

$\Rightarrow$  $65934=P\times \dfrac{11}{10}\times \dfrac{111}{100}$

$\Rightarrow$  $65934=P\times \dfrac{1221}{1000}$

$\Rightarrow$  $P=54\times 1000$

$\therefore$    $P=Rs.54000.$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

What principal will amount to Rs. $38,976$ in two years, if the rates of interest for successive years are $16$% and $20$% respectively?

  1. $27000$
  2. $28000$
  3. $29000$
  4. $30000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$A=P(1+\cfrac{r}{100})^n$
for $r=16$ and $n=1$
$A=P(1+\cfrac{16}{100})^1$
$A=1.16P$
Again for $r=20, n=1,P'=1.16P$
$A=P'(1+\cfrac{r}{100})^n$
$A=1.16P\times 1.2=1.392P\\ A=Rs.38976=1.392P\\ \implies P=28000 $

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Shikkan boy lends Rs.28000 for 4 years at $\displaystyle 6\frac{1}{2}$ per cent per annum and Rs.65500 for 5 years at 8 per cent per annum. Find her total earning from these investments.

  1. $33480$
  2. $34440$
  3. $33240$
  4. $12220$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  Here $P=Rs.28000,\,T=4\,years$ and $R=6\dfrac{1}{2}\%=\dfrac{13}{2}\%$

$\Rightarrow$  $S.I.=\dfrac{P\times R\times T}{100}$

$\Rightarrow$  $S.I.=\dfrac{28000\times 13\times 4}{2\times 100}=Rs.7280$

$\Rightarrow$  Now, $P=Rs.65500,\,T=5\,years$ $R=8\%$

$\Rightarrow$  $S.I.=\dfrac{P\times R\times T}{100}=\dfrac{65500\times 8\times 5}{100}$

$\Rightarrow$  $S.I.=Rs.26,200$.

$\therefore$   Total earning from investment = $Rs.7280+Rs.26,200=Rs.33480$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Calculate the amount and the compound interest on  $5000$ in $2$ years when the rate of interest for successive years is $6\%$ and $8\%$ respectively.

  1. $724$
  2. $727$
  3. $317$
  4. $239$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interest for the $1^{ st }$ year $=Rs$ $\cfrac { 5000\times 1\times 6 }{ 100 } =Rs$ $300$

Amount after $1^{ st }$ year $=Rs$ $5000+Rs$ $300=Rs$ $5300$
Interest for the $2^{ nd }$ year $=Rs$ $\cfrac { 5300\times 1\times 8 }{ 100 } =Rs$ $424$
Amount after $2^{ nd }$ year $=Rs$ $5300+Rs$ $424=Rs$ $5724$
$\therefore$ Compound Interest $=Rs$ $5724-Rs$ $5000= Rs$ $724$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Prem lends Rs. $100,000$ at C.I. for $3$ years. If the rate of interest for the first two years is $15$% per year and for the third year it is $16$%, calculate the sum Rohit will get at the end of the third year.

  1. Rs.$155410$
  2. Rs.$153410$
  3. Rs.$125410$
  4. Rs.$135410$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  $P=Rs.100,000,$ $R _1=15\%$ and $R _2=16\%$

$\Rightarrow$  $A=P\times (1+\dfrac{R _1}{100})^2\times (1+\dfrac{R _2}{100})^1$

$\Rightarrow$  $A=100000\times (1+\dfrac{15}{100})^2\times (1+\dfrac{16}{100})^1$

$\Rightarrow$  $A=100000\times (\dfrac{23}{20})^2\times \dfrac{29}{25}$

$\Rightarrow$  $A=100000\times \dfrac{529}{400}\times \dfrac{29}{25}$

$\Rightarrow$  $A=10\times 529\times 29$

$\therefore$    $A=Rs.153410$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Divide Rs.15,600 into two parts such that the interest on one at 5 percent for 5 years may be equal to that on the other at $\displaystyle 4\frac{1}{2}$ per cent for 6 years.

  1. Rs.$7,400$ and Rs.$8,300$
  2. Rs.$7,700$ and Rs.$8,500$
  3. Rs.$8,700$ and Rs.$7,000$
  4. Rs.$8,100$ and Rs.$7,500$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the parts be $ Rs A  ; Rs  15,600  - A $ 

Simple Interest $ I = \dfrac {PNR}{100} $ 

For the first situation, Given, 

$ P = Rs  A $ 

$ N =5 years $ 

$ R = 5  $ % 

So, $ => I =  \dfrac {PNR}{100} $

$ =>I _1 = \dfrac {A \times 5 \times 5 }{100} $

$ =>I _1= \dfrac {25A}{100} $

For the second situation, Given, 

$ P = Rs 15,600  - A $ 

$ N =6 years $ 

$ R = \dfrac {9}{2} $ % 

So, $ => I =  \dfrac {PNR}{100} $

$ =>I _2  = \dfrac {(15,600  - A) \times 6 \times \dfrac {9}{2}}{100} $

$ =>I _2 =  \dfrac {(15,600  - A) \times 27}{100} $

Given, $ I _1 = I _2 $

$ => \dfrac {25A}{100} = \dfrac {(15,600  - A) \times 27}{100} $

$ 25A = (15,600  - A) \times 27 $

$ 25A = 421200 -27A $

$ => 52A = 421200 $ 

$ => A = Rs  8,100 $ 

And other part $ = Rs 15,600 - Rs 8,100 = Rs  7,500 $ 

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Calculate the amount and the compound interest on  $17000$ in $3$ years when the rate of interest for successive years is $10\%, 10\%$ and $14\%$ respectively.

  1. $6578.70$<span class="MathJax"><span class="MJX_Assistive_MathML">6449.80$
  2. $1700$
  3. $5489.8$
  4. $6449.80$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interest for the $1^{ st } $year $=Rs$ $\cfrac { 17000\times 10\times 1 }{ 100 } =Rs$ $1700$ 

Amount after $1^{ st }$ year $=Rs$ $17000+Rs$ $1700=Rs$ $18700$
Interest for the $2^{ nd }$ year $=Rs$ $\cfrac { 18700\times 10\times 1 }{ 100 } =Rs$ $1870$ 

Amount after $2^{ nd }$ year $=Rs$ $18700+Rs$ $1870=Rs$ $20570$
Interest for the$3^{ rd }$ year $=Rs$ $\cfrac { 20570\times 14\times 1 }{ 100 } =Rs$ $2879.80$ 

Amount after $3^{ rd }$ year $=Rs$ $20570+Rs$ $2879.80=Rs$ $23449.8$
$\therefore$ Compound Interest $=Rs$ $23449.8-Rs$ $17000= Rs$ $6449.80$

Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Rakshat borrows Rs.$16,000$ out of which Rs.$9,000$ at $5\%$ and remaining at $6\%$. Find the total interest paid by him in $4$ years.

  1. Rs.$3,280$
  2. Rs.$3,380$
  3. Rs.$3,480$
  4. Rs.$3,580$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
He borrowed $9000$ at $5$ % and remaining $7000(16000-9000)$ at $6$%
We know that $SI=\cfrac { PRT }{ 100 } $
For $P=9000,R=5,T=4$
$SI=\cfrac { 9000\times 5 \times 4 }{ 100 } =1800$
For $P=7000,R=6,T=4$
$SI=\cfrac { 7000\times 6 \times 4 }{ 100 } =1680$
Total $SI=1800+1680=3480$
$\therefore $ He has to pay Rs.$3480$ at end of $4$ years.
Multiple choice mathematics and statistics interest applying compound interest compound interest formula with different successive rate of interest compound interest ( for different time period)

Calculate the amount and the compound interest on Rs. $12,500$ in $3$ years when the rates of interest for successive years are $8 \%$, $10 \%$ and $10 \%$ respectively. 

  1. Rs. $16,335$ and Rs. $3,835$
  2. Rs. $14,853$ and Rs. $2,353$
  3. Rs. $15,664$ and Rs. $3,164$
  4. Rs. $17952$ and Rs.$5,452$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=Rs.12,500$

$T=3$ years
$R=8 \%,10 \%, 10 \%,$ 
$A=?,C.I.=?$
$A=P\left(1+\cfrac{R}{100} \right )^T$

$=12500\left(1+\cfrac{8}{100}\right)\left(1+\cfrac{10}{100}\right)\left(1+\cfrac{10}{100}\right)$
$=12500\times \cfrac{108}{100}\times \cfrac{110}{100}\times \cfrac{110}{100}$
$=\cfrac{125\times 108\times 121}{100}$
$A=Rs.  16,335$
$C.I.=A-P$
$C.I=16335-12500$
$C.I=Rs. 3835$