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 compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

Vikram borrowed Rs. $20,000$ for $4\dfrac{1}{2}$ years at $10\%$ per annum, compound annually. How much compound interest would he pay at the end of $4\dfrac{1}{2}$ years?

  1. $30711.22$
  2. $20711.22$
  3. $40711.22$
  4. $10711.22$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know the formula,
$A = P\left (1+\dfrac{r}{n}\right)^{n.t}$
Where,
$A =$ total amount
$P =$ principal or amount of money deposited,
$r =$ annual interest rate
$n =$ number of times compounded per year
$t =$ time in years
Given:
$P =$ Rs. $20000, r = 10\%, n = 1$ and $t =$ $4\dfrac{1}{2}$ years
$A = 20000\left (1+\dfrac{0.1}{1}\right)^{1\times 4.5}$
$A = 20000\times 1.1^{4.5}$
$A = 20000\times 1.535561$
$A =$ Rs. $30711.22$
To find interest we use formula $A = P + I$, since $A = 30711.22$ and $P = 20000$ we have:
$A = P + I$
$30711.22 = 20000 + I$
$I = 30711.22 - 20000 = 10711.22$
Interest, I $=$ Rs. $10711.22$

Multiple choice mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

Joshita is having a bank account whose principal is Rs. $12000$ and her bank compounds the interest thrice a year at an interest rate of $15\%$, how much money did she have in her account at the year's end?

  1. $18250.50$
  2. $28250.50$
  3. $38250.50$
  4. $48250.50$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given: $P = 12000, r = 15\%, n = 3$ years
$A = P\left [\left (1+\dfrac{r}{100}\right)^n\right]$
$A = 12000\left [\left (1+\dfrac{15}{100}\right)^3\right]$
$A =$ Rs. $18250.50$

Multiple choice book keeping and accountancy bill of exchange (trade bill) dishonour of a bill dishonour of bills bills of exchange advantages of bill of exchange

On 18.2.13 A drew a bill on B for 10,000. B accepted the bill on 21.2.13. The bill is drawn for 30 days after sight. The due date of the bill will be:

  1. 24.3.13

  2. 22.3.13

  3. 26.3.13

  4. 21.3.13
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a bill 'after sight', the maturity period starts from the date of acceptance (21.2.13). 30 days from 21.2.13 is 23.3.13. Adding 3 days of grace results in 26.3.13.

Multiple choice book keeping and accountancy bill of exchange (trade bill) dishonour of a bill dishonour of bills bills of exchange advantages of bill of exchange

On 1st Jan 2013,  X draws a bill on Y for Rs 1,50,000 for 3 months. X got the bill discounted on 4th Jan 2013, @ 12% p.a. The amount of discount on bill will be:

  1. 4,500

  2. 6,000

  3. 18,000

  4. 3,000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculation of discount for 3 months @ 12% p.a. 

      = 150000* 3/12 * 12/100
      =  4500

Multiple choice book keeping and accountancy bill of exchange (trade bill) dishonour of a bill dishonour of bills bills of exchange advantages of bill of exchange

On 10th Sept. X draws a bill on Y for 3 months for 20,000. $ { 13 }^{ th } $ Dec. Was a sudden holiday, due date of the bill will be:

  1. $ { 11 }^{ th } $ Dec.
  2. $ { 12 }^{ th } $ Dec.
  3. $ { 13 }^{ th } $ Dec.
  4. $ { 14 }^{ th } $ Dec.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If due date comes on emergency holiday need to take next working day as due date therefore here  14th Dec is due date.

Multiple choice book keeping and accountancy bill of exchange (trade bill) dishonour of a bill dishonour of bills bills of exchange advantages of bill of exchange

X draws on Y a bill for 6,00,000 on 1st April for 2 months. Y accepts the bill and sends it to X who gets it discounted for 5,88,000. X immediately remits 1,96,000 to Y. On due date, X being unable to remit the amount due accepts a bill for 8,40,000 for 2 months which is discounted by Y for 8,20,000. Y sends 1,48,000 to X out of the same. How much discount will be borne by X at the time of 1,48,000 remittances.

  1. 12,000.

  2. 18,000.

  3. 11,000.

  4. 8,000.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The discount borne by X is the difference between the face value of the bill and the amount received from the bank. The question asks for the discount on the second bill (8,40,000 discounted for 8,20,000), which is 20,000 total. The remittance logic implies X bears the cost proportional to the funds received.

Multiple choice book keeping and accountancy bill of exchange (trade bill) dishonour of a bill dishonour of bills bills of exchange advantages of bill of exchange

X sold goods to Y on 1st June for 1,50,000. Y immediately accepted a three months bill. On due date Y requested that the bill be renewed for a fresh period of two months. X agrees provided interest at 9% p.a. was paid immediately is cash. What will be the amount of interest in the books of X?

  1. 2,000.

  2. 2,500.

  3. 2,250.

  4. 2,800.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Interest = Principal * Rate * Time. 1,50,000 * 0.09 * (2/12) = 2,250.

Multiple choice book keeping and accountancy bill of exchange (trade bill) dishonour of a bill dishonour of bills bills of exchange advantages of bill of exchange

M sold goods worth of Rs 1,50,000 to N. On 1st Oct, N immediately accepted a three month bill. On due date N requested that the bill be renewed for a fresh period of 3 months. N agrees to pay interest @ 18% p a. in cash. How much interest to be paid in cash by N?

  1. 6,750.

  2. 5,400.

  3. 6,000.

  4. 3,300.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculation of Interest is to be charged @ 18% p.a. for 3 months.

 150000*18/100* 3/12
  6750

Multiple choice book keeping and accountancy bill of exchange (trade bill) dishonour of a bill dishonour of bills bills of exchange advantages of bill of exchange

On 1st Jan, X drew a bill on Y for 3 month for Rs 1,50,000. On 4th March, Y pays the bill to X at 12% p.a. discount, the amount of discount will be?

  1. 1,500

  2. 3,000

  3. 4,500

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

Calculation of discount @12% p.a. for 3 months = 150000 * 12/100 * 3/12

                                                                               = 4500

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

Find the present value of Rs. $10,000$ to be required after $5$ years if the interest rate be $9\%$. Given that $(1.09)^5=1.5386$.

  1. $6,994.42$
  2. $6,949.24$
  3. $6,449.24$
  4. $6,499.42$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, $i=0.09=9\%$
$n=5$
$A _n=10,000$
Required present value $=\displaystyle\frac{A _n}{(1+i)^n}$
$=\displaystyle\frac{10,000}{(1+0.09)^5}$
$=Rs. 6499.42$.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Divide Rs. $6500$ in two parts, such that if one part is lent out at $9\%$ per annum and other at $10\%$ per annum, the total yearly income(income from simple interest) is Rs.$605$.

  1. $2000,\,4000$
  2. $2000,\,4500$
  3. $1500,\,4000$
  4. $1500,\,4500$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the on one part $=x$

      the other part $6500-x$
$\Longrightarrow \dfrac{9x}{100}+\dfrac{6500-x}{100}\times 10=605$
$\Longrightarrow 9x+65000-10x=60500$
$\Longrightarrow x=4500$
$6500-x=6500-4500=2000$

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

Find the amount of an annuity of Rs. 400 per quarter payable for 6 years at 8% p.a.
[Given : $(1.02)^{24} = 1.608$]-

  1. Rs. 11,260

  2. Rs. 12,160

  3. Rs. 13,200

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

Formula for calculating the amount of an annuity,


$F=R \dfrac{\left ( 1+\dfrac{r}{m} \right )^{m \times n} -1}{\dfrac{r}{m}}$

$F=400 \dfrac{\left ( 1+\dfrac{8/100}{4} \right )^{4 \times 6} -1}{\dfrac{8/100}{4}}$

$F=400 \dfrac{\left ( 1+\dfrac{8}{100} \times \dfrac{1}{4} \right )^{24} -1}{\dfrac{8}{100} \times \dfrac{1}{4} }$

$F=400 \dfrac{(1.02)^{24} -1}{\dfrac{1}{50} }$

$F = 12,160$


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

Find the least number of years for which an annuity of Rs. 1,000 must run in order that its amount exceed Rs. 16,000 at 5% p.a. compounded monthly.
[Given : Log 18 = 1.2553, log 105 = 2.8212]

  1. 12 years

  2. 11 years

  3. 13 years

  4. None.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$F=R \dfrac{\left ( 1+\dfrac{r}{m} \right )^{m \times n} -1}{\dfrac{r}{m}}$

$16000=1000 \dfrac{\left ( 1+\dfrac{5}{100} \right )^n -1}{\dfrac{5}{100}}$

$16=1 \dfrac{\left ( 1+\dfrac{5}{100}  \right )^n -1}{\dfrac{5}{100}  }$

$0.8=(1.05)^n-1$

$1.8=(1.05)^n$

Applying log on both sides, we get,

$\log 1.8 = n \log 1.05$

$\Rightarrow n=13$

Least number of years = $13$ years
Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics

A house is sold for $ Rs \ 30,000$ cash or $ Rs\ 17, 500$ cash down payment and instalments of $ Rs \ 1, 600$ per month for eight months. Determine the approximate rate of interest for instalment.

  1. $6.5 \%$
  2. $6 .8 \%$
  3. $ 6. 2 \%$

  4. None of these
  5. $6.3 \%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  Cash price = $Rs.30,000$

$\Rightarrow$  Cash down payment = $Rs. 17500$
$\Rightarrow$  Total amount paid in 8 monthly installments = $Rs.(1600\times 8)=Rs.12800$
$\Rightarrow$  Total amount paid under installment paln = $Rs.17500+Rs.12800=Rs.30300$
$\Rightarrow$  Interest charged = $Rs.30300-Rs.30000=Rs.300$
$\Rightarrow$  Principal for 1st month = $Rs.30000-Rs.17500=Rs.12500$
$\Rightarrow$  Principal for 2nd month = $Rs.12500-Rs.1600=Rs.10900$
$\Rightarrow$  Principal for 3rd month = $Rs.10900-Rs.1600=Rs.9300$
$\Rightarrow$  Principal for 4th month = $Rs.9300-Rs.1600=Rs.7700$
$\Rightarrow$  Principal for 5th month = $Rs.7700-Rs.1600=Rs.6100$
$\Rightarrow$  Principal for 6th month = $Rs.6100-Rs.1600=Rs.4500$
$\Rightarrow$  Principal for 7th month = $Rs.4500-Rs.1600=Rs.2900$
$\Rightarrow$  Principal for 8th month = $Rs.2900-Rs.1600=Rs.1300$
$\Rightarrow$  Total principal = $Rs.55200$
$\Rightarrow$  The last installment of Rs.1600 includes Rs.1300 plus Rs.300 interest.
$\Rightarrow$  Time = 1 month = $\dfrac{1}{12}$year, Interest = Rs.$300$
$\Rightarrow$  Interest = $\dfrac{P\times T\times R}{100}$
$\Rightarrow$  $R=\dfrac{I\times 100}{P\times T}$
$\Rightarrow$  $R=\dfrac{300\times 100}{55200\times \dfrac{1}{12}}=\dfrac{300\times 100\times 12}{55200}=\dfrac{150}{23}=6.5$
$\therefore$   $Rate =6.5\%$

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

Find the present value of an ordinary annuity of $8$ quarterly payments of Rs. $500$ each, the rate of interest being $8\%$ p.a. compounded quarterly.

  1. Rs. $3660.20$
  2. Rs. $3662.50$
  3. Rs. $4275$
  4. Rs. $3660$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $A=$ Rs $500$, $n= 8$

Also, $ r= \dfrac{8}{100} \times \dfrac{1}{4} =0.02 $

$ \therefore V= \dfrac{A}{r} \times \left[1-(1+r)^{(-n)}\right]=\dfrac{500}{0.02} \times \left[1-(1.02)^{(-8)}\right] $

Now, let $ x= (1.02)^{(-8)} $

$\Rightarrow \log{x} = -8\log{1.02}=-8(0.0086) $

$ \Rightarrow \log{x}= -0.0688 $

$ \Rightarrow x= 0.8535 $

$ \Rightarrow  V=\dfrac{500}{0.02} \times [1-0.8535] =$ Rs. $3662.50 $

Thus, the present value of annuity is Rs. $3662.50$.