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

The difference between the C.I. and S.I. on a sum of 7200 for two years is 72. Find the rate of interest per annum.

  1. $10\%$
  2. $12\%$
  3. $15\%$
  4. $20\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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


So, $ SI = \dfrac {7200 \times 2 \times R}{100} = Rs 144R $

When interest is compounded, Amount $ A = P(1+ \dfrac {R}{100})^n $

So, A $ = 7200 \times (1+ \dfrac {R}{100})^2 = Rs  7200 \times (1+ \dfrac {R^2}{10000} + \dfrac {2R}{100})  = Rs 7200 + Rs 0.72R^2 + Rs 144R  $

And $ CI = A - P = Rs 0.72R^2 + Rs 144R $

Si, difference $ CI - SI =  Rs 0.72R^2 + Rs 144R - Rs 144R =  Rs  72 $

$0.72R^2 = 72 $

$R^2 = 100 $ 

So, $ R = 10 $ %

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

A sum is invested at compound interest compounded yearly. If the interest for two successive years be Rs. 5,700 and Rs. 7,410 calculate the rate of interest.

  1. $30\%$
  2. $35\%$
  3. $29\%$
  4. $25\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Difference between the C.I of two successive years=$7410-5700=Rs. 1710$


Rate of interest$=\dfrac{Difference  \ between \ the  \ C.I  \ of \ two \ successive \ year \times100 }{C.I \ of \ preceding   \ year\times time}$


$\therefore$Rate of intereast=$\dfrac{1710\times 100}{5700\times 1}=30$%  

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

A sum of money placed out at compound interest amounts to Rs. 20,160 in 3 years and to Rs. 24,192 in 4 years. Calculate the rate of interest.

  1. 12%

  2. 15%

  3. 20%

  4. 25%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Amount in three year $=Rs. 20160$


Amount in four year $=Rs.24192$

Interest in 1 year $=24192-20160=Rs.4032$

Let the rate of interest $=R$%

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

$\Rightarrow 4032=\dfrac{20160\times R\times 1}{100}$

$\Rightarrow R=\dfrac{4032\times 100}{20160\times 1}=20$%

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

The compouned interest, calculate yearly, on a certain sum of money for the second year is Rs. 1,089 and for the third year it is Rs. 1,197.90. Calculate the rate of interest and the sum of money 

  1. 11%, Rs. 800

  2. 12%, Rs. 400

  3. 13%, Rs. 700

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

Sum after 2 years=Rs.1089

Sum after 3 years=Rs.1197.90
Interest for onr year$=1197.90-1089=108.90$
C.I for 1 year=S.I for 1 year 
$Interest=\frac{PRT}{100}$
$\Rightarrow 108.90=\frac{1089\times R\times 1}{100}$
$\Rightarrow R=\frac{108.90\times 100}{1089}=10$%

Let the sum=Rs.x
Amount=Rs. 1089,Time 2 years,R=10%
$Amount=P\left(1+\frac{R}{100}\right)^t$
$\Rightarrow 1089=x\left(1+\frac{10}{100}\right)^2$
$\Rightarrow 1089=x\times \frac{110}{100}\times \frac{110}{100}$
$\Rightarrow x=\frac{1089\times 100\times 100}{110\times 110}=Rs.900$


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

A certain sum of money is put at compound interest, compounded half-yearly. If the interest for two successive half-years are Rs. 650 and Rs. 760.50; find the rate of interest. 

  1. $34$
  2. $32$
  3. $27$
  4. $38$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Difference between the C.I of two successive half -years=$760.50-650=110.50$

Time =6 months=$\frac{6}{12}=\frac{1}{2}years$
Rate of interest$=\frac{Difference  between  the  C.I  of  two  successive year\times100 }{C.I  of  preceding   year\times time}$

$\therefore$Rate of intereast=$\frac{110.50\times 100\times 2}{650\times 1}=34$%  

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

A certain sum amounts to Rs. 5,292 in two years and Rs. 5,556.60 in three years, interest being compounded annually. Find the rate of interest.

  1. 9%

  2. 15%

  3. 7%

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

Sum after 2 years $=Rs.5292$


Sum after 3 years $=Rs.5556.60$

Interest for onr year $=5556.60-5292=Rs. 264.60$

C.I for 1 year $=$ S.I for 1 year 

$Interest =\dfrac{PRT}{100}$

$\Rightarrow 264.60=\dfrac{5292\times R\times 1}{100}$

$\Rightarrow R=\dfrac{264.60\times 100}{5292}=5$%

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

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 rate of interest per annum.

  1. 12%

  2. 14%

  3. 18%

  4. 22%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$P=Rs.8000$


$Time =\ 1 \ year$


$Amount=9440$

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

$Interest=\dfrac{PRT}{100}$

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

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

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

You invested Rs. $1500$ and received Rs. $5000$ after three years. What had been the interest rate?

  1. $111.11\%$
  2. $222.22\%$
  3. $333.33\%$
  4. $77.77\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Amount invested $= 1500$

Amount received after three years $= 5000$

$\Rightarrow$ Interest earned $= 5000-1500 = 3500$
Let interest rate$\%$ be $r$
$\Rightarrow$ $3500 = \dfrac{1500 \times 3 \times r}{100}$
$\Rightarrow$ $r = 77.77\%$

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

You borrow Rs. $4,000$ from a loan shark. If you owe Rs. $7,200$ in $4$ years, what would be the simple interest rate?

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

Given:
Principal $=$ Rs. $ 4,000$
Interest $= 7200 - 4000 = 3200$
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$\Rightarrow R =$ $\dfrac{3200\times 100}{4000\times 4}$
$\Rightarrow R = 20\%$

Thus, the simple interest rate is $20\%$.

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

John earned Rs. $100$ as simple interest on Rs. $600$ for $6$ months. Find the annual rate of interest.

  1. $11.11\%$
  2. $22.22\%$
  3. $33.33\%$
  4. $44.44\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given, Simple interest $=$ Rs. $100$, Principal $=$ Rs. $600$ and period $6$ months
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$R =$ $\dfrac{100\times 100}{600\times 0.5}$
$R = 33.33\%$
Therefore, the annual rate of interest is $33.33\%$.
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

Sharmila got a Rs. $1300$ loan for $5$ years. She paid Rs. $100$ in interest. What was the interest rate?

  1. $1.1\%$
  2. $1.3\%$
  3. $1.5\%$
  4. $1.7\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given, principal $=$ Rs. $1300$, Interest $=$ Rs. $100$, period $=5$ years
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$\Rightarrow R =$ $\dfrac{100\times 100}{1300\times 5}$
$\Rightarrow R = 1.5\%$
Therefore, the interest rate is $1.5\%$.
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

Find rate, when principal $=$ Rs. $3000$; interest $=$ Rs. $400$; time $= 3$ years.

  1. $1.11\%$
  2. $2.22\%$
  3. $3.33\%$
  4. $4.44\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given, Principal $=$ Rs. $3000$, interest $=$ Rs. $400$, time $=3$ years
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$R =$ $\dfrac{400\times 100}{3000\times 3}$
$R = 4.44\%$

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

Oscar earned Rs. $2400$ as simple interest on Rs. `$4500$ for $3$ months. What is the annual rate of interest?

  1. $16.66\%$
  2. $17.77\%$
  3. $18.88\%$
  4. $19.99\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given, principal $=4500$, Interest $=$ Rs. $2400$, period $=3$ months
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$\Rightarrow R =$ $\dfrac{2400\times 100}{4500\times 3}$
$\Rightarrow R = 17.77\%$
Therefore, the annual rate of interest is $17.77\%$.
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

To start a grocery shop, a woman borrowed Rs. $1,500$. If the loan was for four years and the amount of interest was Rs. $150$, what simple interest rate was she charged?

  1. $1.5\%$
  2. $2.5\%$
  3. $3.5\%$
  4. $4.5\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given, principal $=$ Rs. $1500$, Interest $=$ Rs. $150$, period $=4$ years
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$\Rightarrow R =$ $\dfrac{150\times 100}{1500\times 4}$
$\Rightarrow R = 2.5\%$
Therefore, the simple interest is $2.5\%$.