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

Find the present value of a sequence of annual payments of Rs 25000 each , the first being made at the  end of 5th year and the last being paid at the end of 12th year, if money is worth 6%.

  1. $122875$
  2. $102875$
  3. $132875$

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

We know that formula of present value is 

$V=\cfrac{A}{r}[\cfrac{1}{(1+\cfrac{R}{100})^m}$$-\cfrac{1}{(1+\cfrac{R}{100})^{m+n}}]$
We have  annuity of $8$ terms $(n)$
For $4$ terms $(m)\implies m=4\ \implies m+n=12$
$V=\cfrac{25000}{0.06}[\cfrac{1}{(1+\cfrac{6}{100})^4}$$-\cfrac{1}{(1+\cfrac{6}{100})^{12}}]=Rs.122968.45$

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

A company borrows Rs 10000 on condition to repay it with compound interest at $5$% p.a . by annual instalments at Rs 1000 each. In how many years will the debt be paid off?

  1. 14.2

  2. 21.7

  3. 12.67

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\Rightarrow$  Company borrow Rs.10000 i.e. $pv=Rs.10000$ and $I=5\%=0.05$. $A$ is also given which is $Rs.1000$
$\Rightarrow$  Present value of annuity regular
$\Rightarrow$  $pv=A\times [\dfrac{(1+I)^n-1}{I\times (1+I)^n}]$

$\Rightarrow$  $10000=1000\times [\dfrac{(1+0.05)^n-1}{0.05\times (1+0.05)^n}]$

$\Rightarrow$  $(1.05)^n-0.5\times (0.5)^n=1$
$\Rightarrow$  $(1.05)^n=2$
Taking log both sides
$\Rightarrow$  $n=\dfrac{log\,2}{log\, 1.05}$
$\therefore$   $n=14.2\, years$
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. If at the end of 5th year , he wants to finish his liability by a single payment , how much should he pay?

  1. 90100

  2. 80100

  3. 34504

  4. 54345
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have $A=Rs.5000,\,I=\dfrac{6}{100}\times \dfrac{1}{4}=0.015$ and $n = 20$

$\Rightarrow$  If at the end of 5th year, i.e., at the time of 20th payment, he wants to finish off the liability, then lump sum payment required is,
$\Rightarrow$  $5000$ + Present value of the remaining 20 installments.
$\Rightarrow$  $5000+V$
$\Rightarrow$  $5000$ + $\dfrac{A}{I}[1-(1+I)^{-n}]$

$\Rightarrow$  $5000+\dfrac{5000}{0.015}[1-(0.015)^{-20}]$    ---- ( 1 )

$\Rightarrow$  Let $x=(1.015)^{-20}$
$\Rightarrow$  $log\,x=-20\,log\,(1.015)$
$\Rightarrow$  $log\,x=-20(0.0064)=-0.128=\bar{1}.8720$
$\Rightarrow$  $x=antilog\,(\bar{1}.8720)=0.7447$
Substitute value of $x$ in ( 1 ),
$\Rightarrow$  $5000+\dfrac{5000}{0.015}(1-0.7447)$

$\Rightarrow$  $5000+\dfrac{5000}{0.015}\times 0.2553$

$\Rightarrow$  $Rs.90100$

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

Amit buys a house for Rs 500000. The contract is that amit will pay Rs 200000 immediately and the balance in 15 equal instalments with 15 % p.a compound interest . How much has he to pay annually (approximately)?

  1. Rs$51,305$
  2. Rs$54,005$
  3. Rs$51,843$
  4. Rs$91,305$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Present value $=Rs.50,000Rs.20,000=Rs.30,000$

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

$\implies 30,000=\cfrac{A}{1+(\cfrac{15}{100})}$$+\cfrac{A}{1+(\cfrac{15}{100})^2}+.....$4
$ \implies A\times 5,847 $

$\implies A=Rs51,305$

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

Z invests Rs. $10,000$ every year starting for today for next $10$ years. Suppose interest rate is $8\%$ per annum compounded annually. Calculate future value of the annuity. Given that $(1+0.08)^{10}=2.15892500$.

  1. $1,44,865.625$
  2. $1,56,454.875$
  3. $1,54,654.875$
  4. $1,44,568.625$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Step-$1$: Calculate future value as though it is an ordinary annuity
Future value of the annuity as if it is an ordinary annuity
$=10,000\left[\displaystyle\frac{(1+0.08)^{10}-1}{0.08}\right]$
$=10,000\times 14.4865625$
$=Rs. 1,44,865.625$
Step-$2$: Multiply the result by $(1+i)$
$=1,44,865.625\times (1+0.08)$
$=1,56454.875$.

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

If the interest on $1700$ rupees is $340$ rupees for $2$ year the rate of interest must be

  1. $12\ \%$
  2. $15\ \%$
  3. $4\ \%$
  4. $10\ \%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Principle$=Rs1770\quad\quad Time=2years$

$SI=Rs340\quad\quad Rate=?\ \cfrac{P\times R\times T}{100}=340\Rightarrow \cfrac{1770\times R\times 2}{100}=340\ \Rightarrow R=\cfrac{340\times100}{1770\times2}=\cfrac{340\times5}{177}=9.6\%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

The simple interest on a sum money is 4/9 of the principal and the number of years is equal to the rate percent per annum. The rate per annum is :  

  1. $5$%
  2. $6\dfrac{2}{3}\%$
  3. $6$%
  4. $7\dfrac{1}{5}\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let the principal be $P$.
Rate of interest be $R\%$
According to the question, Time$=R$
Simple interest $=\dfrac{4P}{9}$.
$SI =\dfrac{\left(PTR\right)}{100}$
$\Rightarrow \dfrac{4P}{9} =\dfrac{\left(PTR\right)}{100}$
$\Rightarrow \dfrac{4P}{9} =\dfrac{\left(P\times R\times R\right)}{100}$
$\Rightarrow \dfrac{4P}{9} =\dfrac{\left(P\times {R}^{2}\right)}{100}$
$\Rightarrow \dfrac{4}{9} =\dfrac{{R}^{2}}{100}$
$\Rightarrow {R}^{2}=100\times\dfrac{4}{9}$
$\Rightarrow R= 10\times \dfrac{2}{3}=\dfrac{20}{3}$
Therefore, rate of interest is $\dfrac{20}{3}\%$ or  $6\dfrac{2}{3}\%$.

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is :

  1. Rs. 650

  2. Rs. 690

  3. Rs. 698

  4. Rs. 700

  5. Rs. 715
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

S.I. for $1$ year $= Rs. (854-815) = Rs. 39$


S.I. for $3$ years = Rs. $39 \times 3=Rs. 117$


Therefore,

Principal $= Rs. 815 - Rs. 117 = Rs. 698$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate per cent per annum, will Rs.32000 yield a compound interest of Rs.5044 in 9 months interest being compounded quarterly ?

  1. 25

  2. 23

  3. 20

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Principal = Rs.32000 
Amount $= Rs.(32000 + 5044) = Rs.37044$
Rate $= r\%$ p.a. or $\displaystyle \cfrac{r}{4}\%$ per quarter 
Time = 9 months = 3 quarters i.e., $n = 3$
$\displaystyle \therefore$ Applying $\displaystyle A=P\left ( 1+\cfrac{r}{100} \right )^{n}$ we have
$\displaystyle 37044=32000\left ( 1+\cfrac{r}{400} \right )^{3}\Rightarrow \cfrac{37044}{32000}=\left ( 1+\cfrac{r}{400} \right )^{3}$
$\displaystyle \Rightarrow \cfrac{9261}{8000}=\left ( 1+\cfrac{r}{400} \right )^{3}\Rightarrow \left ( \cfrac{21}{20} \right )^{3}=\left ( 1+\cfrac{r}{400} \right )^{3}$
$\displaystyle \Rightarrow 1+\cfrac{r}{400}=\cfrac{21}{20}\Rightarrow \cfrac{r}{400}=\cfrac{21}{20}-1=\cfrac{1}{20}\Rightarrow r=\cfrac{400}{20}=20\%p.a.$
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate of interest per annum will a sum double itself in 8 years?

  1. $25\%$
  2. $6\frac{1}{4} \%$
  3. $12\frac{1}{2} \%$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

T = 8 years; N = 2; R = ?
R $\times T$ = 100 $\times (N - 1)$


R $\times 8$= 100 $\times (2 - 1)$

$R\, =\, \displaystyle \frac {100}{8}\, =\, 12\frac{1}{2}\, \%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

Simple interest on Rs.2000 for 4 years is Rs.400. Percent rate of interest is

  1. $\displaystyle\frac{2000\times 100}{400\times 4}$
  2. $\displaystyle\frac{400\times 4}{2000\times 100}$
  3. $\displaystyle\frac{400\times 100}{2000\times 4}$

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

Principal = Rs 2000
Time = 4 years
Interest = Rs 400
Now, $Interest = \frac{Principal \times Rate \times Time}{100}$
$400 = \frac{2000\times R\times 4}{100}$
$R = \frac{400 \times 100}{2000 \times 4}$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years?

  1. $4\frac {1}{2}$%
  2. $5\frac {1}{2}$%

  3. 4%

  4. 5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$SI=\frac {2}{5}P, t=10, r=?$
$\frac {Ptr}{100}=\frac {2}{5}P$
or $\frac {10\times r}{100}=\frac {2}{5}$
or $r=\frac {20}{5}=4$%

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A person finds that an increase in the rate of interest from $\displaystyle4\frac{7}{8}$% to $\displaystyle5\frac{1}{8}$% per annum increases his yearly income by Rs 30. His capital in rupees is

  1. 15,000

  2. 14,000

  3. 13,000

  4. 12,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

increase in rate of interest

$4\frac { 7 }{ 8 } =\frac { 39 }{ 8 } $
$5\frac { 1 }{ 8 } =\frac { 41 }{ 8 } $
$\frac { 41 }{ 8 } -\frac { 39 }{ 8 } =\frac { 2 }{ 8 } $
$\frac { 2 }{ 8 } $% of income is Rs30 of the capital
$1$% of income is $\frac { 8 }{ 2 } \times 30$ of capital
$100$% of income will be$\frac { 8 }{ 2 } \times 30\times 100=12000$
His capital in rupees is 12000

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

The time required so that Rs 450 may increase to Rs 576 (the rate of simple interest being 7% per annum) is

  1. 2 years

  2. 3 years

  3. 4 years

  4. 6 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest will be(576-450)=Rs126

 Let the Time required  be t
As per formula,
$Simple\quad Interest=\frac { P\times t\times r }{ 100 } $
$126=\frac { 450\times t\times 7 }{ 100 } $
$315t=1260$
$t=\frac { 1260 }{ 315 } =4$
Time required will be 4 years


Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

If the simple interest on a certain sum of money is $\displaystyle \frac{4}{25}$th of the sum and the rate per cent equals the number of years, then the rate of interest per annum is

  1. $2$%
  2. $4$%
  3. $5$%
  4. $6$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$   Let the principal be $Rs.x$.

$\Rightarrow$   Then, Simple Interest = $\dfrac{4}{25}x.$
$\Rightarrow$    Let the rate of interest per annum be $r\%$ then time ( T)= $r$ years.
$\Rightarrow$   $R=\dfrac{100\times S.I.}{P\times T}$

$\Rightarrow$   $r=\dfrac{100\times \dfrac {4x}{25}}{x\times r}$

$\Rightarrow$   $r^2=\dfrac{400}{25}$

$\Rightarrow$   $r=\dfrac{20}{5}=4\%$