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 banks and simple interest introduction to interests introduction to interest introduction to interest payments

Find the simple interest rate applied to a principal over $5$ years if the total interest paid equals the borrowed principal.

  1. $10\%$
  2. $20\%$
  3. $30\%$
  4. $40\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We have given that interest and borrowed principal are same.

Let $x$ be the interest and borrowed principal.
We know $S.I.=\dfrac{P\times R\times T}{100}$
$\Rightarrow$ $x=\dfrac{x\times R\times 5}{100}$
$\therefore$ $R=\dfrac{100}{5}=20\%$

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

What is the simple interest rate applied to a principal over $2.5$ years if the total interest paid equals the borrowed principal?

  1. $20\%$
  2. $30\%$
  3. $40\%$
  4. $50\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We have given that interest and principal are equal.

Let Rs. $x$ be the interest and principal.
Here $T=2.5$ years
We know $S.I.=\dfrac{P\times R\times T}{100}$
$\Rightarrow$ $x=\dfrac{x\times R\times 2.5}{100}$
$\Rightarrow$ $R=\dfrac{100}{2.5}=40\%$
Therefore, simple interest rate is $40\%$.

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

Jenn borrowed Rs. $5,000$ for $5$ years and had to pay Rs. $1,500$ simple interest at the end of that time. What rate of interest did she pay?

  1. $5$
  2. $6$
  3. $7$
  4. $8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  $P=Rs.5000,\,T=5\,years $ and $S.I.=Rs.1500$

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

$\Rightarrow$  $1500=\dfrac{5000\times R\times 5}{100}$

$\Rightarrow$  $R=\dfrac{1500}{250}$

$\therefore$    $R=6\%$

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

Joshita borrowed Rs. $3,000$ for $3$ years and had to pay Rs.$ 1,000$ simple interest at the end of that time. What rate of interest did she pay?

  1. $11.11$
  2. $22.22$
  3. $33.33$
  4. $44.44$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  $P=Rs.3000,\,T=3\,years$ and $S.I.=Rs.1000$.

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

$\Rightarrow$  $1000=\dfrac{3000\times R\times 3}{100}$

$\Rightarrow$  $R=\dfrac{1000}{90}$

$\therefore$    $R=11.11\%$

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

What rate will amount to Rs. $1,331$ in three years (compounded annually), if the principal amount was Rs $1,000$ respectively? 

  1. $10$%
  2. $11$%
  3. $12$%
  4. $13$%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We have,

$A=Rs.\ 1331$
$P=Rs.\ 1000$
$T=3\ years$
$R=?$

We know that
$A=P\left(1+\dfrac{R}{100}\right)^T$

Therefore,
$1331=1000\left(1+\dfrac{R}{100}\right)^3$

$\dfrac{1331}{1000}=\left(1+\dfrac{R}{100}\right)^3$

$\dfrac{11}{10}=1+\dfrac{R}{100}$

$\dfrac{R}{100}=\dfrac{1}{10}$

$R=10\%$

Hence, this is the answer.

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 $\displaystyle \frac{1}{100}$th of the sum and the rate per cent equals 4 times the number of years, then the rate of interest per annum is

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

$SI=P/100; r=4t \implies t=r/4$

$SI=\cfrac { P\times r\times t }{ 100 } $
$\implies (P/100)=\cfrac { P\times r\times (r/4) }{ 100 } $
$\implies r\times (r/4)=1\ \implies r=2\%$

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

At simple interest a sum of money is double in 20 years. What is the rate of interest?

  1. 20

  2. 4

  3. 5

  4. 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For simple interest, the interest earned is determined by the formula: I = PRT

where I=interest, R=rate, T=time, P=principle
The rate where the interest equals the principle in 20 years. i.e., the amount doubles.
So we know, I=P and T=20 years
so we can solve for R
R=$\dfrac{I}{(P)(T)}$=$\dfrac{I}{P}\times\dfrac{1}{20}$=$1\times\dfrac{1}{20}$=0.05 per year or 5% per year interest.

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

Choose the correct answer from the alternatives given.
Sumit invested Rs. 24000 in a bank for three years. If the rate of interest for 1st, 2nd and 3rd year are 5%, 10% and 4% respectively and the interest is compounded annually, then how much money will be deposited in his account after three years?

  1. Rs. 27,472

  2. Rs. 28,828.80

  3. Rs. 3,45,240

  4. Rs. 5,46,280
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Required sum
= $24000 \left ( 1 + \frac{5}{100} \right )\left ( 1 + \frac{10}{100} \right )\left ( 1 + \frac{4}{100} \right )$
= $Rs.24000 \times 1.05 \times 1.10 \times $ $1.04$
= $Rs. 28828.80$
Hence, Amount after three years is $Rs. 28828.80$

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

A sum of Rs. $46,875$ was lent out as simple interest and at the end of $1$ year $8$ months the total amount was Rs. $50,000$. Find the rate of interest per cent per annum.

  1. $3.5\%$
  2. $4.5\%$
  3. $5\%$
  4. $4\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$A=P(1+it)$
$50,000=46,875\left(1\times i\times 1 \frac{8}{12}\right)$
$i=0.04$; rate $=4\%$

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

The simple and compound interest that can be earned in two year at the same rate is $Rs. 1500$ and $Rs. 1575$ respectively. What is the rate (% per annum) of interest?

  1. $8$
  2. $10$
  3. $12$
  4. $5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
SI CI
$1^{st} Year$ $750$ $750$
$2^{nd} Year$ $750$ $825$

Required rate of interest $= \dfrac {75}{750}\times 100 = 10$

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

A sum of Rs. 1000 is lent to be returned in 11 monthly instalments of Rs. 100 each, interest is simple. The rate of interest is

  1. $9\dfrac{1}{11}$ %
  2. $10\%$
  3. $11\%$
  4. $21\dfrac{9}{11}$ %
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rs. 1000 + S.I. on Rs. 1000 for 11 months
$= Rs. 1000 +$ S.I. on Rs. 100 for $(1+ 2 + 3 + 4 + ... + 10)$ months
Rs. 1000 S.I. on Rs. 100 for 100 months
$= Rs. 1000 +$ S.I. on Rs. $100$ for $55$ months
S.I. on Rs. 100 for 55 months
$= Rs. 100$
$\therefore  Rate = (\cfrac{100\times 100\times 12}{100\times 55})$% $=21\cfrac{9}{11}$ %

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

On a certain Principal if the Simple interest for two years is $Rs.\ 4800$ and Compound interest for the two years is $Rs.\ 5088$, what is the rate of interest

  1. $6\%$
  2. $24\%$
  3. $12\%$
  4. $18\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given,  $SI=4800$
            $CI=5088$
Say the principal amount was $P$ and rate of interest is $r$% p.a for two years
$\therefore$   $SI=\dfrac { PT }{ 100 } =\dfrac { P\times 2\times r }{ 100 } $
$\Rightarrow 4800=\dfrac { 2Pr }{ 100 } $
$\Rightarrow 240000=Pr\quad \longrightarrow \left( 1 \right) $
Similarly $CI=P{ \left( 1+\dfrac { r }{ 100 }  \right)  }^{ 2 }-P$
$\Rightarrow 5088=P\left[ { \left( 1+\dfrac { r }{ 100 }  \right)  }^{ 2 }-1 \right] \quad \longrightarrow \left( 2 \right) $
Substituting $(1)$ in $(2)$ we get
$5088=\dfrac { 240000 }{ r } \left[ 1+\dfrac { { r }^{ 2 } }{ { 100 }^{ 2 } } +\dfrac { 2r }{ 100 } -1 \right] $
$\Rightarrow \dfrac { 5088 }{ 240000 } =\dfrac { r }{ { 100 }^{ 2 } } +\dfrac { 2 }{ 100 } $
$\Rightarrow 0.0212=\dfrac { r }{ { 100 }^{ 2 } } +0.02$
$\Rightarrow 0.0012=\dfrac { r }{ { 100 }^{ 2 } } $
$\therefore$    $r=12$%
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 a sum of $Rs.\ 7500$ amount to $Rs.\ 8427$ in $2$ years compounded annually?

  1. $4$%
  2. $5$%
  3. $6$%
  4. $8$%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We have,
$P=7500\ Rs$
$A=8427\ Rs$
$T=2$ years
$A=P\left (1+\dfrac {R}{100}\right)^T$

$7500+8427=7500\left (1+\dfrac {R}{100}\right)^T$

$\dfrac {8427}{7500}=\left (1+\dfrac {R}{100}\right)^2$

$\left (1+\dfrac {R}{100}\right)=\dfrac {2809}{2500}=\left (\dfrac {53}{50}\right)$

$\left (1+\dfrac {R}{100}\right)=\dfrac {53}{50}-1$

$\dfrac {R}{100}=\dfrac {53}{50}-1$

$R=\dfrac {3}{50}$

$R \ \% = 6\ \%$ 
Hence, this is the answer.