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 maturity value of recurring deposits banking maths

Mr Bittu deposits a certain sum of money each month in a recurring deposit account. If the rate of interest is $8\%$ per annum and Mr Bittu gets Rs $8,088$ from the bank after $3$ years. Find the value of his monthly instalment.

  1. $400$
  2. $800$
  3. $200$
  4. $140$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the monthly installment be $P$

Given, maturity value $=8088$, $n=3$ years $=3\times 12=36$ months, $r=8\%$
Interest $=\dfrac {Pn(n+1)r}{2400}$
$=\dfrac {P\times 36\times 37 \times 8}{2400}$
$=\dfrac {111P}{25}$
We know, amount $=Pn+\dfrac {111P}{25}$
$8088=36P+\dfrac {111P}{25}$
$=\dfrac {1011P}{25}$
$\therefore 8088= \dfrac {1011P}{25}$
$\therefore P=200$
Therefore, monthly installment  is Rs. $200$.

Multiple choice maturity value of recurring deposits banking maths

Divya has a recurring deposit in a bank at $ 5\%$ per annum simple interest. If she pay monthly installment of Rs. $2000$ for annually. Find her Maturity value.

  1. $6049.931$
  2. $6249.931$
  3. $6149.931$
  4. $6549.931$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the formula,
$M =\dfrac{R \times [(1+i)^{n} - 1]}{1-(1+i)^{\dfrac{-1}{3}}}$ 
R $=$ Monthly Installment $= 2000 $
i $=$ Rate of Interest $5\%$
n $=$ Number of Quarters $= 1$
Substitute the values, 
$M =\dfrac{2000 \times [(1+5/400)^{n} - 1]}{1-(1+5/400)^{\frac{-1}{3}}}$ 
$M = \dfrac{2000\times\dfrac{5}{400}}{1-(\dfrac{405}{400})^{-1/3}}$
$M = 6049.931$

Multiple choice maturity value of recurring deposits banking maths

Sheela has a recurring deposit in a bank at $2\%$ per annum simple interest. If she pay monthly installments Rs.$200$ for annually. Find her Maturity value.

  1. $621.99$
  2. $611.99$
  3. $631.99$
  4. $601.99$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the formula,
$M =\dfrac{R \times [(1+i)^{n} - 1]}{1-(1+i)^{\frac{-1}{3}}}$ 
$R =$ Monthly Installment $= 200$ 
$i =$ Rate of Interest/ 400 $= \dfrac {2}{400}$
$n =$ Number of Quarters $= 1$
Substitute the values, 
$M =\dfrac{200 \times [(1+2/400)^{n} - 1]}{1-(1+2/400)^{\frac{-1}{3}}}$ 
$M = \dfrac{200\times\dfrac{2}{400}}{1-(\dfrac{402}{400})^{-1/3}}$
$M = 601.99$

Multiple choice maturity value of recurring deposits banking maths

Rita has a recurring deposit in a bank at $4\%$ per annum simple interest. If she pay monthly installment s Rs.$1000$ for annually. Find her Maturity value.

  1. $3019.97$
  2. $4019.97$
  3. $2019.97$
  4. $5019.97$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the formula,
$M =\dfrac{R \times [(1+i)^{n} - 1]}{1-(1+i)^{\frac{-1}{3}}}$ 
$R $= Monthly Installment $= 1000 $
$i =$ Rate of Interest/ 400 $= \dfrac {4}{400}$
$n =$ Number of Quarters $= 1$
Substitute the values, 
$M =\dfrac{1000 \times [(1+4/400)^{n} - 1]}{1-(1+4/400)^{\frac{-1}{3}}}$ 
$M = \dfrac{1000\times\dfrac{4}{400}}{1-(\dfrac{404}{400})^{-1/3}}$
$M = 3019.97$

Multiple choice maturity value of recurring deposits banking maths

Ahmed has a recurring deposit account in a bank.He deposits Rs $5,500$ per month for 2 years.If he gets Rs $1,46,437.5$ at the time of maturity. Find the interest paid by the bank.

  1. $10.5$%
  2. $30$%
  3. $35$%

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, maturity value $=146437.5$, monthly installment $=5,500$, $n=2$ years $=2\times 12=24$ months

Interest $=\dfrac {Pn(n+1)r}{2400}$
$=\dfrac {5500\times 24 \times 25 \times r}{2400}$
$=1375r$
Therefore, amount $=(Pn+1375r)$
$\Rightarrow 146437.5=(5500\times 24+1375r)$
$\Rightarrow 146437.5=132,000+1375r$
$\Rightarrow 14437.5=1375r$
$\Rightarrow  r=10.5$

Multiple choice maturity value of recurring deposits banking maths

Nithya deposited Rs. $100$ per month for $12$ months in a bank's recurring deposit account. If the bank pays interest at the rate of $10\%$ per annum, find the amount she gets on maturity.

  1. $1205$
  2. $1265$
  3. $1345$
  4. $1450$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given: $P = 100, T(n) = 12$ months, $R = 10\%$
Equivalent principal for $12$ months $=$ $100\times \dfrac{n(n+1)}{2}$
$=$ $100\times\dfrac{12(13)}{2}$
$= 50 \times  12 \times  13$
Interest $=$ $\dfrac{PRT}{100}$
$=$ $\dfrac{50\times 12 \times 13\times 10\times 1}{100\times 12}$
$=$ $65$
Maturity amount $=$ P$\times$T $+$ Interest
$=$ $100 \times 12 + 65$
$=$ Rs. $1265$

Multiple choice maturity value of recurring deposits banking maths

Mohan deposited Rs.$80$ per month in a cumulative deposit account for six years. Find the amount payable to him on maturity, if the rate of interest is $6\%$ per annum.

  1. $6811.20$
  2. $2000$
  3. $4811.20$
  4. $3811.20$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the monthly installment be $P$

Given, monthly installment Rs.$=80$, $r=6\%$, $n=6\times 12=72$
We know, Interest $=\dfrac {Pn(n+1r)}{2400}$
$=\dfrac {80 \times 72 \times 73\times 6}{2400}$
$=\dfrac {5256}{5}$
Required amount $=Pn+{5256}{5}$
$=80 \times 72 +\dfrac {5256}{5}$
$=28800+\dfrac {5256}{5}$
$=6811.20$

Multiple choice maturity value of recurring deposits banking maths

Priya has a recurring deposit in a bank at $10\%$ per annum simple interest. If she pay monthly installment s Rs.$700$ for annually. Find her Maturity value.

  1. $2034.904$
  2. $2134.904$
  3. $3134.904$
  4. $4134.904$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the formula,
$M =\dfrac{R \times [(1+i)^{n} - 1]}{1-(1+i)^{\frac{-1}{3}}}$ 
$R =$ Monthly Installment $= 700 $
$i =$ Rate of Interest/ 400 $= \dfrac {10}{400}$
$n =$ Number of Quarters $= 1$
Substitute the values, 
$M =\dfrac{700 \times [(1+10/400)^{n} - 1]}{1-(1+12/400)^{\frac{-1}{3}}}$ 
$M = \dfrac{700\times\dfrac{10}{400}}{1-(\dfrac{410}{400})^{-1/3}}$
$M = 2134.904$

Multiple choice maturity value of recurring deposits banking maths

Meena has a recurring deposit in a bank at $12\%$ per annum simple interest. If she pay monthly installment s Rs.$400$ for annually. Find her Maturity value.

  1. $1123.92$
  2. $1223.92$
  3. $1623.92$
  4. $1823.92$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the formula,
$M =\dfrac{R \times [(1+i)^{n} - 1]}{1-(1+i)^{\frac{-1}{3}}}$ 
$R =$ Monthly Installment $= 400$ 
$i =$ Rate of Interest/ 400 $= \dfrac {12}{400}$
$n =$ Number of Quarters $= 1$
Substitute the values, 
$M =\dfrac{400 \times [(1+12/400)^{n} - 1]}{1-(1+12/400)^{\frac{-1}{3}}}$ 
$M = \dfrac{400\times\dfrac{12}{400}}{1-(\dfrac{412}{400})^{-1/3}}$
$M = 1223.92$

Multiple choice maturity value of recurring deposits banking maths

An amount of Rs. $20000$ is deposited in a bank for $2$ years and paying an annual interest rate of $5\%$, compounded yearly. Find the maturity value.

  1. $12050$
  2. $22050$
  3. $32050$
  4. $42050$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, principal Amount (P) $=$ Rs. $20000 $ 
Rate of Interest Amount (r) $= 5\% = 0.05  $
Number of Period (t) $= 2$ years 
Compounded Interest (n) $= 1$ (yearly)
Maturity value $=$ $P\times \left (1+\dfrac{r}{n}\right)^{nt}$
$=$ $20000\times \left (1+\dfrac{0.05}{1}\right)^{2}$
$=$ Rs. $22050$

Multiple choice maturity value of recurring deposits banking maths

Sonya deposited Rs. $200$ per month in her bank for six months under the recurring deposit scheme. What will be the maturity value of her deposit, if the rate of interest is $7\%$ per annum and the interest is calculated at the end of every month?

  1. $1936$
  2. $24936$
  3. $3936$
  4. $4936$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given, $P =$ Rs. $200$, $n = 6 $ months, $r = 7\%$
Interest $=$ $\dfrac{Pn(n+1)r}{2400}$

$=\dfrac{200\times6(6+1)7}{100}$
$= 24.5$
Maturity value $= 200 \times  24.5 + 36 =$ Rs. $4936$

Multiple choice maturity value of recurring deposits banking maths

Sneha deposits Rs. $2500$ per month in a bank for $48$ months under a recurring deposit scheme. If she is entitled to get Rs. $150000$ as maturity value, find the rate of interest per annum.

  1. $6\%$
  2. $8\%$
  3. $10\%$
  4. $12\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the rate of interest per annum be $r\%$.
$P =$ Rs. $2500, n = 48$ months
Interest $=$ $\dfrac{Pn(n+1)r}{2400}=\dfrac{2500\times48(48+1)r}{2400}= 2540r$
Maturity amount $ = 2500 \times 48 + 2450r = 120000 + 2450r$
$\Rightarrow 150000 - 120000 = 2450r$
$\Rightarrow 30000 = 2450r$
$\Rightarrow r = 12.24\%$

Multiple choice maturity value of recurring deposits banking maths

John deposited Rs. $50000$ in a bank for $1$ year and paying an annual interest rate of $14\%$, compounded quarterly. What is the maturity amount?

  1. Rs $54548$
  2. Rs $48884$
  3. Rs $84448$
  4. Rs $44888$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, principal Amount $(P)$ $=$ Rs. $50000$  
Rate of Interest Amount $(r)$ $= 14\% = 0.14  $
Number of Period $(t)$ $= 1$ year  
Compounded Interest $(n)$ $= 4$ (quarterly)
Maturity value $=$ $P\times \left (1+\dfrac{r}{n}\right)^{nt}$
$=$ $50000\times \left (1+\dfrac{0.14}{1}\right)^{4}$
$=$ Rs. $84448$

Multiple choice maturity value of recurring deposits banking maths

If the account statement states that the interest is compounded annually then n = ?

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

$A=P(1+\cfrac{r}{100})^n$

Here $n=$ no. of interest periods
If interest is compounded annually
$\implies$ no. of interest period $1\times 1=1$
$\implies n=1$

Multiple choice maturity value of recurring deposits banking maths

The maturity value of a R.D Account is Rs. $16,176$. If the monthly installment is Rs. $400$ and the rate of interest is $8$ $\%$. Find the time period of this R.D account.

  1. $2$ years
  2. $3$ years
  3. $4$ years

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

It is given that

Maturity values $=$ Rs. $16,176$
Monthly installment $=$ Rs. $400$
Rate of interest $=8\%$

Let the time be $x$ months
$\therefore$ Qualifying amount $=\dfrac {400\times (x\times x+1)}{2}=200(x^2+x)$

Now, S.I. $=\dfrac {200(x^2+x)\times 8\times 1}{100\times 12}=\dfrac {2(x^2+x)\times 2}{3}=\dfrac {4}{3}(x^2+x)$

Also, Principal $=$ Rs. $400\times x$

Therefore, $ 400x+\dfrac {4}{3}(x^2+x)=16176$

$\Rightarrow 1200x+4x^2+4x=48528$

$\Rightarrow 4x^2+1204x-48528=0$

$\Rightarrow x^2+301x-12132=0$

$\Rightarrow (x-36)(x+337)=0$

$\Rightarrow x=36$ or $x=-337$

Since the time cannot be negative, we have $x=36$.

The time of RD account is $36$ months or $3$ years.