Quantitative Aptitude

Simple and Compound Interest

3,394 Questions
All Simple interest and its inverse forms 768 Compound interest with annual compounding 742 Simple-interest growth and split sums 626 Difference between compound and simple interest 479 Half-yearly and quarterly compounding 252 Changing rates and fractional years 201 Installments (CI based) 190 Ratio of principal to interest 118 Population growth and depreciation 16

Simple and Compound Interest Questions

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

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.

Multiple choice maturity value of recurring deposits banking maths

Kiran deposited Rs.$200$ per month for $36$ months in a bank's recurring deposit account. If the bank pays interest at the rate of $11$ $\%$ per annum, find the amount she gets on maturity.

  1. Rs.$8412$
  2. Rs.$8421$
  3. Rs.$2481$
  4. Rs.$1234$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the monthly installment be $P$.

Given, $P=200$, $n=36$, $r=11\%$
Interest $=\dfrac {Pn(n+1)r}{2400}$$=\dfrac {200\times 36 \times 37\times 11}{2400}$$=1221$
We know, maturity amount $=(Pn+1221)$$=(200\times 36+1221)$$=$ Rs. $8421$

Multiple choice investement and financial planning banking compound interest comparing quantity maths

The price of a T.V. set worth Rs. 20,000 is to be paid in 20 instalments of Rs. 1000, each. If the rate of interest be 6% per annum, and th6 first instalment be paid at the time of purchase, then, the value of the last instalment covering the interest as well will be : (Hotel Management, 1998)

  1. Rs. 1050

  2. Rs. 2050

  3. Rs. 3000

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

The question is complex and often appears in competitive exams with specific annuity formulas. Given the structure of 20 installments of 1000, the final payment must account for the remaining principal and interest.

Multiple choice investement and financial planning banking compound interest comparing quantity maths

Mr. Dua invested money in two schemes P and Q offering compound interest @ 8 p.c.p.a. and 9 p.c.p.a respectively. if the total amount of interest accrued two schemes together in two years was Rs 4818.30 and the total amount invested was Rs 27, 000, what was the amount invested in Scheme P?

  1. Rs 12, 000

  2. Rs 13,500

  3. Rs 15, 000

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

Let p invested Rs x Then q invested Rs $(27000-x)$
$\therefore x(1+\dfrac{8}{100})^{2}-1+(27000-x)(1+\dfrac{9}{100})^{2}-1=4818.30$
$\Rightarrow (x\times \dfrac{104}{625})+\dfrac{1881(27000-x)}{10000}= \dfrac{481830}{100}$
$\Rightarrow 1664x+1881(27000-x)=48183000$
$\Rightarrow (1881x-1664x)=50787000-48183000$
 Or $217x=2604000$
  Or $x=12000 Rs$

Multiple choice investement and financial planning banking compound interest comparing quantity maths

A family made a down payment of \$75 and borrowed a set of encyclopedias that cost \$400. The balance with interest was paid in 23 monthly payments of \$16 each and a final payment of \$9. What was the per cent of interest to the borrowed sum?

  1. 12 %

  2. 14 %

  3. 16 %

  4. 18 %
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total cost =\$ 400
Down payment=\$ 75
Remaining amount=$400-75=$ 325\$
Balanced paid in 24 months=\$23 \times 16+9=$ 377$
Difference=$377-325=$52$
The per cent of interest to the borrowed sum=$\frac{52}{325}\times 100=16$


Multiple choice investement and financial planning banking compound interest comparing quantity maths

A man borrows Rs. $200$ at $ 5$% compound interest. At the end of each year he pays back Rs. $50$. At the end of $4 $ years he owes

  1. Rs. $27.59$
  2. Rs. $28.10$
  3. Rs. $27.81$
  4. Rs. $28.14$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Amount of one year

$\displaystyle=200\left[1+\frac{5}{100}\right]$

$\displaystyle=200\times\frac{21}{20}=210$

$\therefore$ At the end of year he pays back Rs. 50. So the principal for the second year is Rs. 160.
$\therefore$ Amount of Second year

$\displaystyle=160\left[1+\frac{5}{100}\right]$

$\displaystyle=160\times\frac{21}{20}=168$

$\therefore$ At the end of year he pays back Rs. 50. 
So rest amount = 168 -50 = Rs. 118.
This amount is principal amount for third year.
$\therefore$ Amount of third year

$\displaystyle=118\left[1+\frac{5}{100}\right]$

$\displaystyle=118\times\frac{21}{20}=123.90$

At the end of years he pays back Rs. 50.
So rest amount
$=123.90-50=Rs. 73.90$
This amount is principal for fourth year.
$\therefore$ Amount of fourth year

$\displaystyle=73.90\left[1+\frac{5}{100}\right]$

$\displaystyle=73.90\times\frac{21}{20}=77.59$

At the end of year he pays back Rs. 50.
So rest amount
$=77.595-50=Rs. 27.59$
$\therefore$ At the end of fourth year he owes Rs. 27.59.

Multiple choice investement and financial planning banking compound interest comparing quantity maths

Lakshman borrowed Rs. $20$ lakhs as housing loan from ICICI at $10\%$ p.a to be repaid in $10$ years. if the EMI is Rs. $2500$ per lakh, find how much he pays as interest in the first month. Find also he principal repaid then.

  1. Rs. $33333.34$
  2. Rs. $33344.64$
  3. Rs. $36543.45$
  4. Rs. $54600$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interest at $10\%$ for the first month for Rs. $20$ lakhs $=$ $2000000 \times \dfrac{1}{12}\times \dfrac{10}{100}=16666.66$
EMI for one month, for $20$ lakhs $= 2500 \times  20 =$ Rs. $50000$
Hence principal repaid $=$ Rs. $50000 - 16666.66 =$ Rs. $33333.34$

Multiple choice investement and financial planning banking compound interest comparing quantity maths

A sum of Rs $550$ was taken as a loan. This is to be paid back in two equal instalments. If the rate of interest be $20\%$ compounded annually, then the amount of each instalment will be

  1. Rs $360$
  2. Rs $350$
  3. Rs $340$
  4. Rs $300$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let $x$ be each installment
After paying the first installement $x$
the remaininng principle is $ 550\times1.2-x$
This then compounded yearly should be equal to the second installment
$\left(550\times1.2-x\right)\times 1.2= x$
$ 550\times 1.2^2-x\times 1.2 = x$
$792=2.2\times x$
$x=360$
Thus eachn installemnt should be $Rs.360$
Multiple choice investement and financial planning banking compound interest comparing quantity maths

A television set is sold for Rs. $10000$ cash on Rs. $2000$ cash down followed by six equal instalments of Rs. $1600$ each. What is the rate of interest?

  1. $50\%$
  2. $60\%$
  3. $70\%$
  4. $80\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $n = 6, I =$ Rs. $1600$, 

$E = 2000 + 6 \times  1600 - 10000 = $ Rs. $1600$
We know $R = \dfrac{2400E}{n(n+1)I-2E}$
$\Rightarrow R = \dfrac{2400\times 1600}{6(6+1)1600-2\times 1600}$
$\Rightarrow R = 60\%$
Thus, the rate of interest is $60\%$.

Multiple choice investement and financial planning banking compound interest comparing quantity maths

Raghav buys a shop for $Rs. 1,20,000$. He pays half of the amount in cash and agrees to pay the balance in $12$ annual installments of $Rs. 5000$ each. If the rate of interest is $12\%$ and he pays with the installment the interest due on the unpaid amount find the total cost of the shop.

  1. $Rs. 1,60,800$
  2. $Rs. 1,66,800$
  3. $Rs. 1,68,800$
  4. $Rs. 1,60,000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given that: 
Raghav buys a shop for $Rs.1,20,000.$
He pays half of the amount in cash $= \dfrac{120000}{2}\Rightarrow Rs.60,000$

Balance amount to be paid $= 120000 - 60000 \Rightarrow Rs. 60000.$

Given that amount of each installment $=Rs. 5000.$

He agrees to pay the balance in $12$ annual installments with interest of $12\%.$

 Amount of the $1^{st}$ installment 
$\Rightarrow 5000 + \dfrac{12}{100}\times   60000$

$\Rightarrow 5000 + 600 \times 12$

$\Rightarrow 5000 + 7200$

$\Rightarrow Rs. 12,200.$


 Amount of the $2^{nd}$ installment
$ \Rightarrow 5000 + \dfrac{12}{100} \times (60000 - 5000)$
$\Rightarrow 5000 + \dfrac{12}{100}\times  55000$
$\Rightarrow 5000 + 550 \times 12$
$\Rightarrow 5000 + 6600$
$\Rightarrow Rs. 11,600.$

As the amount paid for installment is $12200,11600,....... $ so It forms an $AP.$

The first term $a = 12,200$
Common Difference $d =  11600 - 12200\Rightarrow-600$
Total number of terms $n = 12.$

We know that sum of $n$ terms in $AP$
$\Rightarrow \dfrac{n}{2}[2a + (n-1) d]$

 Therefore the total cost of the shop
 $\Rightarrow 60000 +\dfrac{ 12}{2}[2(12200) + (12-1) \times (-600)]$

$\Rightarrow 60000 + 6(24400 - 6600)$
$\Rightarrow 60000 + 6 \times 17800$
$\Rightarrow 60000 + 106800$
$=Rs. 1,66,800.$

Hence, the total cost of the shop $= Rs.1,66,800.$