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 simple and compound interest that can be earned in two year at the same rate is $Rs. 1500$ and $Rs. 1575$ respectively. What is the rate (% per annum) of interest?

  1. $8$
  2. $10$
  3. $12$
  4. $5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
SI CI
$1^{st} Year$ $750$ $750$
$2^{nd} Year$ $750$ $825$

Required rate of interest $= \dfrac {75}{750}\times 100 = 10$

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

A sum of Rs. 1000 is lent to be returned in 11 monthly instalments of Rs. 100 each, interest is simple. The rate of interest is

  1. $9\dfrac{1}{11}$ %
  2. $10\%$
  3. $11\%$
  4. $21\dfrac{9}{11}$ %
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rs. 1000 + S.I. on Rs. 1000 for 11 months
$= Rs. 1000 +$ S.I. on Rs. 100 for $(1+ 2 + 3 + 4 + ... + 10)$ months
Rs. 1000 S.I. on Rs. 100 for 100 months
$= Rs. 1000 +$ S.I. on Rs. $100$ for $55$ months
S.I. on Rs. 100 for 55 months
$= Rs. 100$
$\therefore  Rate = (\cfrac{100\times 100\times 12}{100\times 55})$% $=21\cfrac{9}{11}$ %

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

On a certain Principal if the Simple interest for two years is $Rs.\ 4800$ and Compound interest for the two years is $Rs.\ 5088$, what is the rate of interest

  1. $6\%$
  2. $24\%$
  3. $12\%$
  4. $18\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given,  $SI=4800$
            $CI=5088$
Say the principal amount was $P$ and rate of interest is $r$% p.a for two years
$\therefore$   $SI=\dfrac { PT }{ 100 } =\dfrac { P\times 2\times r }{ 100 } $
$\Rightarrow 4800=\dfrac { 2Pr }{ 100 } $
$\Rightarrow 240000=Pr\quad \longrightarrow \left( 1 \right) $
Similarly $CI=P{ \left( 1+\dfrac { r }{ 100 }  \right)  }^{ 2 }-P$
$\Rightarrow 5088=P\left[ { \left( 1+\dfrac { r }{ 100 }  \right)  }^{ 2 }-1 \right] \quad \longrightarrow \left( 2 \right) $
Substituting $(1)$ in $(2)$ we get
$5088=\dfrac { 240000 }{ r } \left[ 1+\dfrac { { r }^{ 2 } }{ { 100 }^{ 2 } } +\dfrac { 2r }{ 100 } -1 \right] $
$\Rightarrow \dfrac { 5088 }{ 240000 } =\dfrac { r }{ { 100 }^{ 2 } } +\dfrac { 2 }{ 100 } $
$\Rightarrow 0.0212=\dfrac { r }{ { 100 }^{ 2 } } +0.02$
$\Rightarrow 0.0012=\dfrac { r }{ { 100 }^{ 2 } } $
$\therefore$    $r=12$%
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate per cent per annum will a sum of $Rs.\ 7500$ amount to $Rs.\ 8427$ in $2$ years compounded annually?

  1. $4$%
  2. $5$%
  3. $6$%
  4. $8$%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We have,
$P=7500\ Rs$
$A=8427\ Rs$
$T=2$ years
$A=P\left (1+\dfrac {R}{100}\right)^T$

$7500+8427=7500\left (1+\dfrac {R}{100}\right)^T$

$\dfrac {8427}{7500}=\left (1+\dfrac {R}{100}\right)^2$

$\left (1+\dfrac {R}{100}\right)=\dfrac {2809}{2500}=\left (\dfrac {53}{50}\right)$

$\left (1+\dfrac {R}{100}\right)=\dfrac {53}{50}-1$

$\dfrac {R}{100}=\dfrac {53}{50}-1$

$R=\dfrac {3}{50}$

$R \ \% = 6\ \%$ 
Hence, this is the answer.
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A sum of money compounded annually amounts to 1375 in 5 years and 1980 in 7 years. Find the annual rate of interest.

  1. 12%

  2. 20%

  3. 15%

  4. 10%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

interest is compounded, Amount $ A = P(1+ \frac {R}{100})^n $
So, for the first situation
$ 1375 = P \times (1+ \frac {R}{100})^5 $   - (1)

And for the first situation
$ 1980 = P \times (1+ \frac {R}{100})^7 $   ---- (2)

Dividing eqn 2 by eqn 1, we get
$ \frac {1980}{1375} =   (1+ \frac {R}{100})^2 $ 
$ => \frac {396}{275} =   (1+ \frac {R}{100})^2 $ 
$ => \frac {36}{25} =   (1+ \frac {R}{100})^2 $ 
$ => (1+ \frac {R}{100}) = \frac {6}{5} $
$ => \frac {R}{100} = \frac {1}{5} $
$ => R =20 $ %

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

The difference between the interest earned under compound interest, interest being compounded annually and simple interest for two years on the same sum and at the same rate of interest is 25.60. Find the sum if the rate of interest is 8% p.a

  1. 2000

  2. 2500

  3. 3200

  4. 4000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation



Simple Interest $ SI = \frac {PNR}{100} $
So, $ SI = \frac {P \times 2 \times 8}{100} = Rs 0.16P $

When interest is compounded, Amount $ A = P(1+ \frac {R}{100})^n $
So, A $ = P \times (1+ \frac {8}{100})^2 = Rs  1.1664P  $
And $ CI = A - P = 0.1664P $

Si, difference $ CI - SI = Rs 0.1664P - Rs 0.16P = Rs 25.60 $
$ => 0.0064P = 25.60 $
$ => P = Rs  4000 $

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

If the simple interest on a certain sum of money is $\displaystyle \frac{1}{100}$th of the sum and the rate per cent equals the number of years, then the rate of interest per annum is

  1. $2$%
  2. $1$%
  3. $3$%
  4. $4$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given $SI=\cfrac { 1 }{ 100 } \times P,R=T$
$SI=\cfrac { PRT }{ 100 } $
$\cfrac { P }{ 100 } =\cfrac { P{ R }^{ 2 } }{ 100 } \Rightarrow R=T=1$
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

The interest on a certain sum of money is $0.18$ times of itself in $3$ years. Find the rate of interest.

  1. $4$
  2. $5$
  3. $6$
  4. $7$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$I=Interest$

$P=Principal$
$R=Rate of Interest$
$T=Time(in years)$
$0.18I=\dfrac { I\times R\times 3 }{ 100 } \ \Rightarrow R=\dfrac { 0.06\times 100 }{ 3 } =0.06\times 100\$
 $\Rightarrow R=6$ %
Rate of Interest $= 6$%

Multiple choice commercial studies money loans from banks and financial institutions introduction to money - barter system owned fund and borrowed fund

_______ of a given sum of money due at the end of a certain period of time is that sum which if invested now at the given rate of interest accumulates to the given sum at the end of the period.

  1. Annuity

  2. Interest

  3. The present value

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

The present value is the current worth of a future sum of money or stream of cash flows given a specified rate of return.

Multiple choice instruments of monetary policy and the reserve bank of india money and banking economics

RBI can very CRR between _________.

  1. $5 \ to \ 15\%$
  2. $3 \ to \ 15\%$
  3. $5 \ to \ 12\%$
  4. $4 \ to \ 10\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cash Reserves Ratio (CRR) refers to the proportion of total deposits of the commercial banks which they must keep as reserves with the central bank in the form of cash. Cash reserve ratio is determined by central bank so that they can control the amount of credit creation of the commercial banks at the time of inflation or deflation in the economy. By the order of the parliament, Reserve Bank of India(RBI) can vary the cash reserve ratio between 3 to 15% of the total deposits of the commercial banks.