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

If the amount is $2 \dfrac{1}{4}$ times the sum after 2 years at compound interest, the rate of interest, per annum is 

  1. 25%

  2. 30%

  3. 40%

  4. 50%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interest is compounded annually,

So amount, $A=P\left ( 1+\dfrac{r}{100} \right )^{t}$

Where $P$ is Principal (or sum)
$t$ is time (in years)
$A$ is the amount, person will get after time $t$
and $r$ is rate of interest per annum

Here $A=2\dfrac{1}{4}P=\dfrac{9}{4}P$
and $t=2$ years

Now apply the formula,
$A=P\left ( 1+\dfrac{r}{100} \right )^{t}$

$\dfrac{9}{4}P=P\left ( 1+\dfrac{r}{100} \right )^{2}$

$\Rightarrow \dfrac{9}{4}=\left ( 1+\dfrac{r}{100} \right )^{2}$

Square root both sides,

$\dfrac{3}{2}=\left ( 1+\dfrac{r}{100} \right )$

$\dfrac{r}{100}=\dfrac{3}{2}-1=\dfrac{1}{2}$

$r=\dfrac{100}{2}=50$%

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

Find the money which when invested for $1.5$ years and compounded annually at the rate of $8$% per annum, amounts to Rs. $175.37.$

  1. $168.21$
  2. $156.13$
  3. $159.36$

  4. none
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$T=1.5$ ,$R=8\%$,Amount$=175.37$
we know that,
$A=P\left(1+\dfrac{R}{100}\right)^{T} $
$\implies175.37=P\left(1+\dfrac{8}{100}\right)^{1.5}$
$P=\dfrac{175.37}{1.12}=156.13$
Multiple choice mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

Calculate the amount and compound interest on Rs. $62,500$ for $1\frac{1}{2}$ years at 8% per annum compounded half yearly.

  1. Amount =Rs. 70304, compound interest=Rs. 7804

  2. Amount =Rs. 70304, compound interest=Rs. 7404

  3. Amount =Rs. 70204, compound interest=Rs. 7804

  4. Amount =Rs. 70442, compound interest=Rs. 7804
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here, Principal =Rs. 62,500
Rate =8% per annum =4% half year
Time =$1\frac{1}{2}$ years =3 half years
$Amount = P(1 +\frac{R}{100})^T$
$\therefore Amount =Rs.[62500\times {(1+\frac{4}{100})}^{3}]$
$Amount = \displaystyle(62500\times \frac{104}{100}\times \frac{104}{100}\times \frac{104}{100}) =Rs. 70304$
$\therefore$ Compound interest =Rs.(70304-62500)=Rs.7804

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

Compound interest at 5% per annum is charged on Rs.1000. The prinicipal for the second year is

  1. Rs.1025

  2. Rs.1050

  3. Rs.1075

  4. Rs.1102
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Principal = Rs 1000
time = 1 year
Rate = 5 %


The amount at the end of the first year is equal to the principal at the end of the second year.

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

$\Rightarrow A = 1000 \left(1 + \dfrac{5}{100}\right)^1$

$\Rightarrow A = \dfrac{1000\times 105 }{100}$

$\Rightarrow A = Rs\,  1050$

Thus, Principal for second year = $Rs 1050$

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

A sum of money placed at C. I. doubles itself in 5 years. It will amount to eight times itself in ............

  1. 15 years

  2. 20 years

  3. 12 years

  4. 10 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the amount Rs 100 and rate of interest r
By hypothesis
$200=100(1+\frac{r}{100})^{5}$
$\Rightarrow 2=(1+\frac{r}{100})^{5}$
$\Rightarrow (1+\frac{r}{100})=2^{\frac{1}{5}}$
Lets amount become 8 time in n years then
$800=100(1+\frac{r}{100})^{n}$
$\Rightarrow 8=(1+\frac{r}{100})^{n}$=$(2^{\frac{1}{5}})^{^{n}}$
$\Rightarrow (2)^{3}$=$ (2)^{\frac{n}{5}}$
$\therefore \frac{n}{5}=3$ 
OR n=15 years

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

A man borrow Rs. 10,000 at 5% per annum compound interest. He repays 35% of the sum borrowed at the end of the first year and 42% of the sum borrowed at the end of the second year. How much must be pay at the end of the third year in order to clear the debt?

  1. Rs. 3,398.50

  2. Rs. 3,371.50

  3. Rs. 3,333.50

  4. Rs. 3,307.50
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For the first year

$P _1=10,000$,R=5%
$A _1=10,000(1+\frac{5}{100})$
       $=10000\times \frac{105}{100}$
       $=Rs.  10500$
At the end of the first year he repay 35% of the sum borrowed so he repay the amount$=10000\times \frac{35}{100}=Rs 3500$
left amt$=10000-3500=Rs.  7000$
For the second year
$P _2=Rs.7000$, R=5%
$A _2=7000(1+\frac{5}{100})$
       $=7000\times \frac{105}{100}$
       $=Rs.   7350$
At the end of the second year he repay 42% of the sum borrowed so he repay the amt=$10000\times \frac{42}{100}=Rs.  4200$
Left amt$=7350-4200=Rs.   3150$
For the Third year
$P _3=Rs.  3150$,R=5%
$A _3=3150(1+\frac{5}{100})$
       $=3150\times \frac{105}{100}$
       $=Rs.  3307.50$
Hence he pay Rs. 3307.50 at the end of the third year in order to clear the debt.


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

Calculate the amount and the compound interest on:
Rs. 8,000 for $1\dfrac{1}{2}$ years at 10% per annum compounded yearly.

  1. Rs. 9,230 and Rs. 1,230

  2. Rs. 10,000 and Rs. 2,000

  3. Rs. 9,735 and Rs. 1,735

  4. Rs. 8,442 and Rs. 442
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Amount $A=P(1+r)^{t}$


Here, $P=8000, r=\dfrac{10}{100}=0.1, t=1\dfrac12=\dfrac32=1.5$

$\therefore A=8000(1+0.1)^{1.5}$
         $=8000(1.1)^{1.5}$
         $=8000(1.1537)$
         $=9230$

Compound interest$=9230-8000=1230$

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

Saurabh invests Rs. 48,000 for 7 year at 10% per annum compound interest. Calculate: The interest for the first year.

  1. Rs. 4,800

  2. Rs. 4,900

  3. Rs. 5,000

  4. Rs. 5,100
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P=Rs.48000$


$Rate=10%$


$Time =1 year$

C.I for 1 year=S.I for 1 year$=\dfrac{PRT}{100}$

$\Rightarrow \dfrac{48000\times 10\times 1}{100}=Rs.4800$

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

A sum of Rs. $13,500$ is invested at $16\%$ per annum compound interset for $5$ years. Calculate the amount at the end of the first year

  1. Rs. 15,660

  2. Rs. 17,890

  3. Rs. 19,535

  4. Rs. 20,990
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Sum=Rs.13500$


$Rate=16%$

Amount at the end of first year$=P\left(1+\dfrac{R}{100}\right)^T$

$\Rightarrow 13500\left(1+\dfrac{16}{100}\right)$

$\Rightarrow 13500\times \dfrac{116}{100}=Rs.15660$

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

Ramesh invests Rs. 12,800 for three years at the rate of 10% per annum compound interest. Find the sum due to Ramesh at the end of the first year

  1. Rs. $14,080$
  2. Rs. $15,691$
  3. Rs. $17,776$
  4. Rs. $148,342$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Principal$=Rs.12800$


Rate$=10$%

Time$=1$ year

C.I for 1 year $=$ S.I for 1 year$=\dfrac{PRT}{100}$

$\Rightarrow \dfrac{12800\times 10\times 1}{100}=Rs.1280$

$Amount=P+S.I=12800+1280=Rs.14080$

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

A sum of Rs. $13,500$ is invested at $16\%$ per annum compound interset for $5$ years. Calculate the interest for the first year

  1. Rs. $2,690$
  2. Rs. $2,460$
  3. Rs. $2,230$
  4. Rs. $2,160$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$P=13500$

$R=16$%
$T=1 year$

$\Rightarrow$ C.I for 1 year $=$ S.I of 1 year $=\dfrac{13500\times 16\times 1}{100}=Rs.2160$

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

Saurabh invests Rs. 48,000 for 7 year at 10% per annum compound interest. Calculate: The interest for the third year 

  1. Rs. 6,411

  2. Rs. 5,808

  3. Rs. 5,269

  4. Rs. 4,922
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$Sum=rs.48000$


$Rate=10%$

$Time =2 \ year$

Amount after 2 year
$Amount=P\left(1+\dfrac{R}{100}\right)^t$

$\Rightarrow 48000\left(1+\dfrac{10}{100}\right)^2$

$\Rightarrow 48000\times \dfrac{110}{100}\times \dfrac{110}{100}=Rs.58080$

For third  year

$Sum=58080$

$Time =1 \ year$

Then amount after 3rd year$=58080\left(1+\dfrac{10}{100}\right)$

$\Rightarrow 58080\times \dfrac{110}{100}=Rs.63888$

$\therefore $Interest for third year$=63888-58080=Rs.5808$

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

Ramesh invests Rs. 12,800 for three years at the rate of 10% per annum compound interest. Find the interest he earns for the second year.

  1. Rs. 1,162

  2. Rs. 1,243

  3. Rs. 1,408

  4. Rs. 1,591
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P $=Rs.12800$


Rate of interest $=10$ %

Interest for the first year $=\dfrac{PRT}{100}$

$\Rightarrow \dfrac{12800\times 10\times 1}{100}=Rs.1280$

Amount after first year$=12800+1280=Rs.14080$

For Second year
Principal $=Rs.14080$
R $=10$%
T $=1$ year

then Interest for second year$=\dfrac{PRT}{100}$

$\Rightarrow \dfrac{14080\times 10\times 1}{100}=Rs.1408$