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 maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

Divide Rs 7053 into three parts so that the amount after 2, 3 and 4 years respectively may be equal, the rates of interest being 4% per annum. 

  1. Rs 2500, Rs 3500, Rs 1053

  2. Rs 2436, Rs 2349, Rs 2268

  3. Rs 2568, Rs 3200, Rs1285

  4. Rs 2360, Rs 2289, Rs 2404
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Take the parts as x, y & z.

Then x+y+z=7053.
Obtain the the respective amounts for x,y & z, which are equal, for the 
given years.
Now solve for x, y & z.

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

Find the amount of Rs 12000 after 2 years compounded annually the rate of interest being 5 % pa during the first year and 6% pa during the second year also find the compound interest?

  1. Rs 1356

  2. Rs 1200

  3. Rs 1256

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

P=Rs.12000,Time=2 Years,Rate=5% and 6%
$A=P\left(1+\frac{R}{100}\right)^T$
$\Rightarrow 12000\left(1+\frac{5}{100}\right)\left(1+\frac{6}{100}\right)$
$\Rightarrow 12000\times \frac{105}{100}\times \frac{106}{100}$
$\Rightarrow 13356  Rs$
$C.I=A-P$
$\Rightarrow 13356-12000=1356  Rs.$

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

A man borrowed Rs.$60,000$ for $2$ years at $8$ % per year compound interest. 

Calculate the final amount at the end of the second year.

  1. Rs. $68,984$
  2. Rs. $69,744$
  3. Rs. $69,910$
  4. Rs. $69,984$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\Rightarrow$  $P=$Rs.$60000,\,T=2\,$years and $R=8\%$


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

$\Rightarrow$  $A=60000\times (1+\dfrac{8}{100})^2$

$\Rightarrow$  $A=60000\times (\dfrac{27}{25})^2$

$\Rightarrow$  $A=60000\times \dfrac{729}{625}$

$\therefore$     $A=$Rs. $69,984.$

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

A sum of Rs. $8,000$ is invested for $3$ years at $10 \%$ per annum compound interest. Calculate the interest for the second year.

  1. $440$
  2. $880$
  3. $330$
  4. $800$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $P=$ Rs. $8,000,\,R=10\%$.

Interest for second year $=$ $P\times \dfrac{R}{100}\times \left (1+\dfrac{R}{100}\right)$
$=$ $8000\times \dfrac{10}{100}\times \left (1+\dfrac{10}{100}\right)$
$=$ $800\times \dfrac {11}{10}$
Therefore, interest for second year $=$ Rs. $880.$

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

In what time will Rs, $15,000$ yield Rs. $4965$ as compound interest at $10$% per year compounded annually?

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

Interest for the first year 

$=\cfrac{1500\times 10\times 1}{100}$
$=$ Rs $1500$
Amount after the first year $=$ Rs $15000+1500$
$=$ Rs $ 16500$ 
Interest for the second year
$=$ $\cfrac{16500\times 10\times 1}{100}$
$=$ Rs $1650$
Amount after the third year 
$=$ $\cfrac{18150\times 10\times 1}{100}$
$=$ Rs $1815$
Final amount $= $ Rs $18150+1815$
$=$ Rs $19965$
Compound interest $=$ Rs $19965-15000$
 $=$ Rs $4965$
Required time $= 3$ years

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

Find the compound interest on Rs. $70,000$ for $2$ years, compounded annually at $10\%$ per annum.

  1. $14,400$
  2. $14,700$
  3. $14,300$
  4. $14,100$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here,$P=$ Rs $7000$ , $R=10\%p.a$

interest for the first year $=\cfrac{P\times R\times T}{100}$
$=\cfrac{7000\times 10\times 1}{100}$
$=$ Rs $7000$
The amount after the first year $=$ Rs $77000$
Principal for the second year $=$ Rs $77000$
Interest for the second year $=$ Rs $\cfrac{77000\times 10\times 1}{100}$
$=$ Rs $7700$
The final amount $=$ Rs $77000$ + Rs $7700$
$=$ Rs $84700$
Compound interest $= $ Rs $84700 -70000$
$=$ Rs $14700$
                                                 


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

A finance company declares that, with compound interest rate, a sum of money deposited by anyone will become $8$ times in three years. if the same amount is deposited at the same compound-rate of interest, then in how many years it will become $128$ times?

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

In three years.a sum of money deposited by anyone will become $=2^3=8$times

Therefore , to make sum of money $128$ times , then $2^7=128$, it will occcur in $7$ years.

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

A sum of Rs.$12,000$ is invested for $3$ years at $18$ % per annum compound interest. Calculate the interest for the third year.

  1. $2700$
  2. $2800$
  3. $2900$
  4. $3000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Interest for the first year =$ \cfrac{12000 \times 1 \times 18}{100} = 2160$

Amount after first year = $12000+2160 =14160$
Interest for second year =$ \cfrac{14160 \times 1 \times 18}{100} = 2550$
Amount after second year = $14160+2550 =16708.8$

Interest for third year =$ \cfrac{16708.8 \times 1 \times 18}{100} = 3000(approx)$

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

The compound interest on $Rs. 64,000$ for $3$ years, compounded annually at $7.5$% per annum is

  1. $Rs. 14,400$
  2. $Rs. 15,705$
  3. $Rs. 15,507$
  4. $Rs. 15,075$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$Principal = 64000$
$Rate = 7.5\% \,p.a$
$Time = 3 years$ 
$\text{Where r is the rate and t is the time.}$
$CI = 64000 (1 + 7.5/100)^3 - 64000$
$= 64000 (1 + 75/1000)^3 - 64000$
$= 64000 (1 + 3/40)^3 - 64000$
$= 64000 (43/40)^3 - 64000$
$= 64000 * 43/40 * 43/40 * 43/40 - 64000$
$= 43 * 43 * 43 - 64000$
$= 79507 - 64000$
$= 15507$
$\text{Hence CI will be 15507 rupees}$

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

Priyanka borrowed $Rs8,000$ at $12\%$ simple interest for $3$years and lent it to Renu for $3$ years at $15\%$ per annum compound interested, compounded annually, Priyanka's profit at the end of $3$ years is

  1. $Rs.2,880$
  2. $Rs.1,287$
  3. $Rs.4,167$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Priyanka's simple interest paid on borrowing Rs 8,000 at 12 percent for 3 years is SI = (8000 * 12 * 3) / 100 = Rs 2,880. The amount received by lending it at 15 percent compound interest compounded annually for 3 years is A = 8000 * (1 + 0.15)^3 = 8000 * 1.520875 = Rs 12,167. The compound interest earned is 12,167 - 8,000 = Rs 4,167. Priyanka's profit is the difference between interest earned and interest paid: 4,167 - 2,880 = Rs 1,287.

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

The compound interest on $Rs5,000$ at $4\%$ per annum for $2$ years compounded annually will be

  1. $Rs806$
  2. $Rs708$
  3. $Rs5,408$
  4. $Rs408$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Compound interest can be calculated using the formula Amount = P(1 + r/100)^n. For principal P = 5000, rate r = 4%, and time n = 2 years, the total amount is 5000 * (1 + 4/100)^2 = 5000 * (26/25)^2 = 5408. The compound interest is the total amount minus the principal, which equals 5408 - 5000 = 408.

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 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.