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

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 $2.5\%$.
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

Mr. Joshua borrowed Rs. $5000$ for $2$ years to make home improvements. If he repaid a total of Rs. $15,000$, at what interest rate did he borrow the money?

  1. $15\%$
  2. $25\%$
  3. $35\%$
  4. $45\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given:
Principal $= 5,000$
Interest $= 15000 - 5000 = 10000$
We know the formula,
Rate of interest, $R =$ $\dfrac{I\times 100}{PT}$
$\Rightarrow R =$ $\dfrac{5000\times 100}{10000\times 2}$
$\Rightarrow R = 25\%$

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

Peter invests $ $5,000$ at $4$% simple annual interest. How much in his investment worth after $2$ months?

  1. 5323.66

  2. 5033.33

  3. 5066.33

  4. 5343.67
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If the principal amount is $p$, annual interest is $r$ $\%$ then for simple interest after $n$ years the amount will be $p\left (1+\dfrac {nr}{100}\right)$.
Here $p=5000$, $n=\dfrac {1}{6}$, $r=4$ $\%$
So, the amount after $2$ months is $5000\left (1+\dfrac {2}{300}\right) = 5000\left (\dfrac {151}{150}\right) = 5033.33$

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

The difference between compound interest and simple interest on an amount of Rs. $15,000$ for $2$ years is Rs. $96$. What is the rate of interest per annum?

  1. $8$
  2. $10$
  3. $12$

  4. Cannot be determined

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

$\left [15000\times \left (1 + \dfrac {R}{100}\right )^{2} - 15000\right ] - \left (\dfrac {15000\times R\times 2}{100}\right ) = 96$
$\Rightarrow 15000 \left [\left (1 + \dfrac {R}{100}\right )^{2} - 1 - \dfrac {2R}{100}\right ] = 96$
$\Rightarrow 15000 \left [\dfrac {(100 + R)^{2} - 10000 - (200\times R)}{10000}\right ] = 96$
$\Rightarrow R^{2} = \left (\dfrac {96\times 2}{3}\right ) = 64$
$\Rightarrow R = 8$.
$\therefore Rate = 8$%.

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

Ramesh borrowed $Rs \ 14000$ from a bank on simple interest for a period of $5$ years. He returned $Rs \ 6000$ to the bank at the end of three years and $Rs \ 10,900$ at the end of the five years and closed the account. Find the rate of interest per annum.

  1. $4 \%$
  2. $4.14 \%$
  3. $6 \%$
  4. $9 \%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We have,

$P=Rs.\ 14000$

Ramesh returned $Rs.\ 6000$ to the bank at the end of $3$ years.

And returned $Rs.\ 10, 900$ to the bank at the end of $5$ years.

So, the total amount returned by Ramesh is $6000+10,900=Rs.\ 16, 900$

$T=5\ years$
$R=?$

We know that
$A-P=\dfrac{PRT}{100}$ 

So,

$16900-14000=\dfrac{14000\times R\times 5}{100}$ 

$2900=140\times R\times 5$ 

$R=4.14\%$

Hence, this is the answer.

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 $8$ years if the total interest paid equals the borrowed principal.

  1. $10\%$
  2. $20\%$
  3. $12.5\%$
  4. $15\%$
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 $T=8$ years
We know $S.I.=\dfrac{P\times R\times T}{100}$
$\Rightarrow$ $x=\dfrac{x\times R\times 8}{100}$
$\Rightarrow$ $R=\dfrac{100}{8}=12.5\%$
Simple interest rate is $12.5\%$.