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 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

Present value of annuity, $(V)$, can be found by

  1. $ V=\dfrac{r}{A} \times \left[1-(1+r)^{(-n)}\right] $
  2. $ V=\dfrac{A}{r} \times \left[1-(1+r)^{(-n)}\right] $
  3. $ V=\dfrac{A}{r} \times \left[1-(1+r)^{(n)}\right] $
  4. $ V=\dfrac{r}{A} \times \left[1-(1+r)^{(n)}\right] $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The present value annuity factor is used for simplifying the process of calculating the present value of an annuity. A table is used to find the present value per dollar of cash flows based on the number of periods and rate per period. Once the value per dollar of cash flows is found, the actual periodic cash flows can be multiplied by the per dollar amount to find the present value of the annuity.
$v= \frac{A}{r} \times [1-(1+r)^{(-n)}]$
where , A =annuity , r =rate per period , n= number of periods

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. $3662.50$.

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

A man borrowed some money and returned it in $3$ equal quarterly installments of Rs. $4630.50$ each. What sum did he borrow if the rate of interest was $20\%$ p.a. compounded quarterly?

  1. Rs. $12000$
  2. Rs. $12100$
  3. Rs. $12160$
  4. Rs. $13000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, we have to find present value $(V)$ of an ordinary annuity certain.

Given, $A=$ Rs. $4630.50$, $n= 3$

Also $ r= \dfrac{20}{100} \times \dfrac{1}{4}=0.05 $

$ \therefore V=\dfrac{A}{r} \times [1-(1+r)^{(-n)}] $

$=\dfrac{4630.50}{0.05} \times [1-(1.05)^{(-3)}]$

$=$ Rs. $12610 $

Thus, the sum borrowed was Rs. $12160$.

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

Find the Amount 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. $3670$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, $A=$ Rs. $500$, $n= 8$

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

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

Let $ x= (1.02)^(8) $

$\Rightarrow \log{x}=8\log{1.02}=0.0688 $

$ \Rightarrow x= 1.171 $

$ \Rightarrow  M= \dfrac{500}{0.02} \times [1.171-1] =$ Rs $4275 $

Thus, the amount is Rs. $4275$.

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

A man borrows Rs $37500$ and agrees to repay in semi-annual installments of Rs $2250$ each, the first due in $6$ months. How many payments must he make if rate of interest is $6\%$ compounded semi-annually?

  1. $23$
  2. $24$
  3. $25$
  4. $22$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  Here, we have to find the number of payments, $n$.

$\Rightarrow$  $V=Rs.37500$  and $A=Rs.2250$
$\Rightarrow$  Rate of interest compounded semi-annually = $\dfrac{1}{2}\times 6\% = \dfrac{1}{2}\times \dfrac{6}{100}=0.03$
$\Rightarrow$  $V=\dfrac{A}{r}\times [1-(1+r)^{-n}]$

$\Rightarrow$  $37500=\dfrac{2250}{0.03}\times [1-(1.03)^{(-n)}]$

$\Rightarrow$  $1-(1.03)^{-n}=\dfrac{37500\times 0.03}{2250}$

$\Rightarrow$  $(1.03)^{(-n)}=0.5$

$\Rightarrow$  $-n\, log(1.03)=log(0.5)$

$\Rightarrow$  $-n(0.0128)=-0.3010$

$\Rightarrow$  $n=\dfrac{-0.3010}{-0.0128}$

$\therefore$    $n=23.51 \approx 24$

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

Find the Present value of an annuity due of Rs $500$ per quarter for $8$ years and $9$ months at $6\%$ compounded quarterly.

  1. Rs $27032.30$
  2. Rs $23137.98$
  3. Rs $13740.86$
  4. Rs $24017.25$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, rate of interest, r =$1.5$% per interest period =$0.015$
Number of interest periods, $n = 4 \times 8 +3 = 35$
Each installment, $A=Rs $ $500$
Present value of annuity due,
$v = \dfrac{A}{r} \times (1+r) \times [1-(1+r)^{-n}]$

= $\dfrac{500}{0.015} \times 1.015 \times [1-(1.015)^{-35}]$
= $13740.86$

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

A man borrowed some money and returned it in $3$ equal quarterly installments of Rs $4630.50$ each. Find the interest charged (in Rs) on the sum he borrowed, if the rate of interest was $20\%$ p.a. compounded quarterly?

  1. $1731.50$
  2. $1200$
  3. $1300$
  4. $1251.80$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here, we have to find present value $(V)$ of an ordinary annuity certain.

Given, $A=$ Rs $4630.50$, $n= 3$

Also $ r= \dfrac{20}{100} \times \dfrac{1}{4}=0.05 $

$ \therefore V=\dfrac{A}{r} \times [1-(1+r)^{(-n)}] =\dfrac{4630.50}{0.05} \times [1-(1.05)^{(-3)}]=$ Rs. $ \: 12610 $

Thus, the sum borrowed was Rs. $12160$

Now, total money repaid $ = 3 \times 4630.50 =$ Rs. $ \: 13891.50 $

Therefore, interest paid $ =$ Rs, $ \: 13891.50$ $-$  Rs. $ \: 12160 =$ Rs. $ \: 1731.50 $.

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

Find the amount of an annuity due of Rs $500$ per quarter for $8$ years and $9$ months at $6\%$ compounded quarterly.

  1. Rs $27452.30$
  2. Rs $23137.98$
  3. Rs $13740.86$
  4. Rs $24671.30$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Number of interest periods, $n = 4 \times 8 +3 = 35$
Each installment, A=Rs $500$
Present value of annuity due,
$v = \frac{A}{r} \times (1+r) \times [1-(1+r)^{-n}]$
= $\frac{500}{0.015} \times 1.015 \times [1-(1.015)^{-35}]$
= $13740.86$
$v = \frac{A}{r} \times (1+r) \times [1-(1+r)^{-n}-1]$
= $\frac{500}{0.015} \times 1.015 \times [1-(1.015)^{-35}-1]$
= $23137.98$

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

Three equal instalments each of $Rs 200$ were paid at the end of the year for the sum borrowed at $20 \%$ interest compounded annually. Find the sum. 

  1. $ 600$
  2. $421.3$
  3. $ 400$
  4. $ 431.1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Each Installment = $\dfrac{P{\cdot}r}{100[1-{\{ \dfrac{100}{100+r} \}}^n]}$
Here Installement$ = 200$
Rate of interest $(r) = 20%$
Number of years$ (n) = 3$
Solving the above equation gives $P = 421.3$

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

Find the present value (in Rs) of a sequence of annual payments of Rs $10000$ each, the first being made at the end of $5^{th}$ year and the last being made at the end of $12^{th}$ year, if money is worth $6\%$.

  1. $40187.38$
  2. $49087.38$
  3. $40107.38$
  4. $49187.38$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, we have a deferred annuity of $8$ terms(n), deferred for $4$ terms.Each installment, A=Rs $10000$
Rate of interest, $r=$ $6\%$= $0.06$
m= $4$, $m + n=$ $12$
Using the formula, present value
$V = \dfrac{A}{r}$ $\times \dfrac{1}{(1+r)^m}$ - $\frac {1}{(1+r)^{m+n}}$
$V = \dfrac{10000}{0.06} \times [(1.06)^{-4}-(1.06)^{-12}]$$ =49187.38$

Multiple choice business mathematics and statistics insurance and annuity amount of an annuity annuities financial mathematics
Find SI if, Amount =  $Rs \ 1120$ , Rate = $2\dfrac{2}{5}\%$ per year , Time = $5$ years 
  1. $1200$
  2. $201$
  3. $120$
  4. $134.4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$ SI= prt$

$p$ is the principal amount on which interest is to be calculated
$r$ is the rate of interest at which the loan is taken
$t$ is the time period for which the simple interest is to be calculated
From the question we know that,
$p=Rs 1120, $ $r =2.4$ percent and $t=5$ years
$\Rightarrow SI = (1120)(2.4)(0.01)(5)= 134.4$

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

A sum of Rs $2500$ is invested at a rate of $5 \%$ per annum for a term of $5$ years. Find the simple interest received at the end of the term.

  1. $1250$
  2. $625$
  3. $1200$
  4. $1500$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  Here, $P=Rs.2500,\, R=5\%,\, T=5\,years$.

$\Rightarrow$  $Simple\, Interest=\dfrac{P\times R\times T}{100}$
$\Rightarrow$  $\dfrac{2500 \times 5\times 5}{100}$
$\Rightarrow$  $25\times 25$
$\therefore$  $Simple\, Interest\, =Rs.625$

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

A $5-$year ordinary annuity has a present value of $\$1,000$.  If the interest rate is $8$ percent, the amount of each annuity payment is closest to which of the following? 

    1. $ $250.44$
    2. $ $231.91$
    3. $ $181.62$
    4. $ $184.08$
    5. $ $170.44$
    Reveal answer Fill a bubble to check yourself
    A Correct answer
    Explanation

    $\Rightarrow$   We have, $V=\$1000\, r=8\%=0.08$ and $n=5$

    $\Rightarrow$  $V=\dfrac{A}{r}\times [1-(1+r)^{-n}]$
    $\Rightarrow$  $A=\dfrac{V\times r}{1-(1+r)^{-n}}$

    $\Rightarrow$  $A=\dfrac{1000\times 0.08}{1-(1.08)^{-5}}$

    $\therefore$     $A=\$250.44$