Simple and Compound Interest Questions PDF
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Question 1: What is the difference (in Rs) between compound interest (compounded annually) and simple interest for 3 years on a principal of Rs 3000 at the annual rate of 20% ?
a) 464
b) 384
c) 356
d) 424
Question 2: The difference between simple interest on a certain sum at the rate of 8% per annum for 18 months and 24 months is Rs 452. What is the sum (in Rs)?
a) 10500
b) 14600
c) 11300
d) 13600
Question 3: Simple interest on a sum for 10 years is equal to 5% of the principal. In how many years interest will be equal to the principal?
a) 100
b) 150
c) 200
d) 250
Question 4: A sum of money invested at simple interest becomes $\frac{13}{10}$ of itself in 2 years and 6 months. What is the rate (in percentage) of interest per annum?
a) 10
b) 15
c) 12
d) 18
Question 5: The simple interest on a sum of money is $\frac{16}{25}$ of the principal. The number of years is equal to the rate of interest per annum. What is the rate (in percentage) of interest per annum?
a) 4
b) 16
c) 8
d) 12
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Question 6: A sum of Rs 5000 becomes Rs 8000 in 3 years, when invested in a scheme of simple interest. If the same sum is invested in a scheme of compound interest with same yearly interest rate (compounding of interest is yearly), then what will be the amount (in Rs) after 3 years?
a) 8640
b) 8260
c) 8880
d) 9220
Question 7: The simple interest on a sum is $\frac{5}{9}$ of the principal for 25 years. What is the rate (in percentage) of interest per annum?
a) $\frac{25}{9}$
b) $\frac{9}{2}$
c) $\frac{20}{9}$
d) $\frac{15}{4}$
Question 8: Simple interest on a sum of Rs 67400 for 14 months is Rs 4718. What is the rate (in percentage) of interest per annum?
a) 5.5
b) 6
c) 8
d) 7
Question 9: Some part of Rs 17500 was lent at the rate of 24% per annum simple interest and the remaining part at the rate of 10% per annum simple interest. The total interest received after 5 years is Rs 13300. What is the ratio of money lent at the rate of 24% and 10%?
a) 12 : 13
b) 3 : 4
c) 3 : 2
d) 13 : 22
Question 10: A sum of Rs 4000 becomes Rs 5800 in 3 years, when invested in a scheme of simple interest. If the same sum is invested in a scheme of compound interest with same yearly interest rate (compounding of interest is done yearly), then what will be the amount (in Rs) after 2 years?
a) 4430
b) 5450
c) 5290
d) 4970
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Question 11: The difference between the simple interest and compound interest (compounded annually) on Rs. 40,000 for 3 years at 8% per annum is
a) Rs.684.32
b) Rs.788.48
c) Rs.784.58
d) Rs.4000
Question 12: The difference between compound interest and simple interest on a certain sum of money for 2 years at 5% per annum is Rs. 41. What is the sum of money?
a) Rs.7200
b) Rs.9600
c) Rs.16400
d) Rs.8400
Question 13: The difference between simple and compound interest (compounded annually) on a sum of money for 3 years at 10% per annum is Rs. 93. The sum (in Rs.) is:
a) 30000
b) 30300
c) 3000
d) 3030
Question 14: The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525 . The simple interest on the same sum for double the time at half the rate percent per annum is :
a) Rs.520
b) Rs.550
c) Rs. 500
d) Rs. 515
Question 15: The compound interest on Rs. 64,000 for 3 years, compounded annually at 7.5% p.a. is
a) Rs. 14,400
b) Rs. 15,705
c) Rs. 15,507
d) Rs. 15,075
Question 16: The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. The rate of interest per annum is?
a) 6%
b) 7%
c) 8%
d) 9%
Question 17: The amount of Rs. 10,000 after 2 years, compounded annually with the rate of interest being 10% per annum during the first year and 12% per annum during the second year, would be (in rupees)
a) 11,320
b) 12,000
c) 12,320
d) 12,500
Question 18: The difference between the compound interest and the simple interest on Rs. 6250 at 8% per annum in 2 years is
a) Rs.30
b) Rs.40
c) Rs.50
d) Rs.60
Question 19: The difference between compound interest and simple interest on Rs. 5000 for 2 years at 8% per annum payable yearly is
a) Rs.30
b) Rs.31
c) Rs.33
d) Rs.32
Question 20: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs. 1. The sum (in Rs.) is:
a) 620
b) 630
c) 640
d) 625
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Answers & Solutions:
1) Answer (B)
Principal sum = Rs. 3,000
Rate of interest = 20% and time period = 3 years
=> Difference between compound and simple interest = $[P(1+\frac{R}{100})^T-P]-(\frac{P \times R\times T}{100})$
= $[3000(1+\frac{20}{100})^3-3000]-(\frac{3000 \times 20\times 3}{100})$
= $[3000(\frac{6}{5})^3-3000]-(1800)$
= $3000\times(\frac{216}{125})-4800$
= $(24\times216)-4800$
= $5184-4800=Rs.$ $384$
=> Ans – (B)
2) Answer (C)
Let the sum be = Rs. $100x$
Rate of interest = 8%
=> Simple interest = $\frac{P\times R\times T}{100}$
According to ques,
=> $(\frac{100x\times8\times2}{100})-(\frac{100x\times8\times1.5}{100})=452$
=> $16x-12x=452$
=> $x=\frac{452}{4}=113$
$\therefore$ Sum = $100\times113=Rs.$ $11,300$
=> Ans – (C)
3) Answer (C)
Let principal amount = Rs. $100x$
=> Simple interest = $\frac{5}{100}\times100x=Rs.$ $5x$
Let rate of interest = $r\%$ and time period = 10 years
=> Simple interest = $\frac{P\times R\times T}{100}$
=> $\frac{100x\times r\times10}{100}=5x$
=> $10r=5$
=> $r=\frac{5}{10}=0.5\%$
Let the interest will be equal to the principal in = $t$ years at 0.5% rate
=> $\frac{100x\times 0.5\times t}{100}=100x$
=> $t=\frac{100}{0.5}=200$ years
=> Ans – (C)
4) Answer (C)
Let sum of money invested = Rs. $100x$
=> Amount under simple interest = $\frac{13}{10}\times100x=Rs.$ $130x$
Thus, simple interest = $130x-100x=Rs.$ $30x$
Let rate of interest = $r\%$ and time period = 2.5 years
=> Simple interest = $\frac{P\times R\times T}{100}$
=> $\frac{100x\times r\times2.5}{100}=30x$
=> $2.5r=30$
=> $r=\frac{30}{2.5}=12\%$
=> Ans – (C)
5) Answer (C)
Let sum of money invested = Rs. $100x$
=> Simple interest = $\frac{16}{25}\times100x=Rs.$ $64x$
Let rate of interest = time period = $x$
=> Simple interest = $\frac{P\times R\times T}{100}$
=> $\frac{100x\times x\times x}{100}=64x$
=> $x^2=64$
=> $x=\sqrt{64}=8\%$
=> Ans – (C)
6) Answer (A)
Principal sum = Rs. 5000 and time period = 3 years
=> Amount after simple interest = Rs. 8000
Thus, simple interest = Rs. (8000-5000) = Rs. 3000
Let rate of interest = $r\%$
=> Simple interest = $\frac{P\times R\times T}{100}$
=> $\frac{5000\times r\times3}{100}=3000$
=> $150r=3000$
=> $r=\frac{3000}{150}=20\%$
$\therefore$ Amount under compound interest = $P(1+\frac{R}{100})^T$
= $5000(1+\frac{20}{100})^3$
= $5000(1+\frac{1}{5})^3=5000(\frac{6}{5})^3$
= $5000\times\frac{216}{125}$
= $40\times216=Rs.$ $8640$
=> Ans – (A)
7) Answer (C)
Let principal amount = Rs. $9x$
=> Simple interest = $\frac{5}{9}\times9x=Rs.$ $5x$
Let rate of interest = $r\%$ and time period = 25 years
=> Simple interest = $\frac{P\times R\times T}{100}$
=> $\frac{9x\times r\times25}{100}=5x$
=> $\frac{9r}{4}=5$
=> $x=\frac{5\times4}{9}=\frac{20}{9}\%$
=> Ans – (C)
8) Answer (B)
Principal sum = Rs. 67,400 and simple interest = Rs. 4718
Let rate of interest = $r\%$ and time period = $\frac{14}{12}=\frac{7}{6}$ years
=> Simple interest = $\frac{P\times R\times T}{100}$
=> $\frac{67,400\times r\times7}{6\times100}=4718$
=> $\frac{4718r}{6}=4718$
=> $r=6\%$
=> Ans – (B)
9) Answer (D)
Let sum lent for 24% = Rs. $100x$ and sum lent for 10% = Rs. $(17500-100x)$
Time period = 5 years
=> Simple interest = $\frac{P\times R\times T}{100}$
According to ques,
=> $\frac{100x\times24\times5}{100}+\frac{(17500-100x)\times10\times5}{100}=13300$
=> $120x+(175-x)\times50=13300$
=> $120x+(175\times50)-50x=(175\times76)$
=> $70x=175(76-50)$
=> $x=\frac{175\times26}{70}=65$
$\therefore$ Required ratio = $\frac{100\times65}{17500-(100\times65)}$
= $\frac{6500}{11000}=\frac{65}{110}=13:22$
=> Ans – (D)
10) Answer (C)
Principal sum = Rs. 4000 and time period = 3 years
=> Amount after simple interest = Rs. 5800
Thus, simple interest = Rs. (5800-4000) = Rs. 1800
Let rate of interest = $r\%$
=> Simple interest = $\frac{P\times R\times T}{100}$
=> $\frac{4000\times r\times3}{100}=1800$
=> $120r=1800$
=> $r=\frac{1800}{120}=15\%$
$\therefore$ Amount under compound interest = $P(1+\frac{R}{100})^T$
= $4000(1+\frac{15}{100})^2$
= $4000(1+\frac{3}{20})^2=4000(\frac{23}{20})^2$
= $4000\times\frac{529}{400}$
= $10\times529=Rs.$ $5290$
=> Ans – (C)
11) Answer (B)
Principal (P) = Rs. 40,000
Rate of interest (r) = 8% and time period (t) = 3 years
Simple interest = $\frac{P \times r \times t}{100}$
= $\frac{40,000 \times 8 \times 3}{100}$
= $400 \times 24=Rs.$ $9600$
Compound interest = $P[(1+\frac{r}{100})^t-1]$
= $40,000[(1+\frac{8}{100})^3-1]$
= $40,000[(\frac{27}{25})^3-1]$
= $40,000 (\frac{19683-15625}{15625})=40,000 \times \frac{4058}{15625}$
= $Rs.$ $10388.48$
$\therefore$ C.I. – S.I. = $10388.48-9600=Rs.$ $788.48$
=> Ans – (B)
12) Answer (C)
Let the given sum = Rs. $100x$
Rate of interest = 5% and time period = 2 years
Compound interest = $P [(1 + \frac{R}{100})^T – 1]$
= $100x [(1 + \frac{5}{100})^2 – 1]$
= $100x [(\frac{21}{20})^2 – 1] = 100x (\frac{441 – 400}{400})$
= $100x \times \frac{41}{400} = 10.25x$
Simple interest = $\frac{P \times R \times T}{100}$
= $\frac{100x \times 5 \times 2}{100} = 10x$
=> Difference between simple and compound interests = $10.25-10x = 41$
=> $0.25x = 41$
=> $x = \frac{41}{0.25} = 164$
$\therefore$ Value of given sum = $100 \times 164 = Rs. 16,400$
13) Answer (C)
Let the given sum = Rs. $1000x$
Rate of interest = 10% and time period = 3 years
Compound interest = $P [(1 + \frac{R}{100})^T – 1]$
= $1000x [(1 + \frac{10}{100})^3 – 1]$
= $1000x [(\frac{11}{10})^3 – 1] = 1000x (\frac{1331 – 1000}{1000})$
= $1000x \times \frac{331}{1000} = 331x$
Simple interest = $\frac{P \times R \times T}{100}$
= $\frac{1000x \times 10 \times 3}{100} = 300x$
=> Difference between simple and compound interests = $331-300x = 93$
=> $31x = 93$
=> $x = \frac{93}{31} = 3$
$\therefore$ Value of given sum = $1000 \times 3 = Rs. 3,000$
14) Answer (C)
Let the sum = Rs. $100x$
For compound interest, rate of interest (r) = 10% and time (t) = 2 years
=> $C.I. = P[(1+\frac{r}{100})^t-1]$
=> $100x[(1+\frac{10}{100})^2-1]=525$
=> $100x[(\frac{11}{10})^2-1]=525$
=> $100x \times (\frac{121-100}{100})=525$
=> $21x=525$
=> $x=\frac{525}{21}=25$
$\therefore$ Sum invested = Rs. 2500
For simple interest, rate of interest (r) = 5% and time (t) = 4 years
=> $S.I.= \frac{P \times r \times t}{100}$
= $\frac{2500 \times 5 \times 4}{100}$
= $25 \times 20=Rs.$ $500$
=> Ans – (C)
15) Answer (C)
Principal (P) = Rs. 64,000
Time (t) = 3 years and rate of interest under compound interest (r) = 7.5%
=> $C.I. = P[(1+\frac{r}{100})^t-1]$
= $64000[(1+\frac{7.5}{100})^3-1]$
= $64000[(1+\frac{15}{200})^3-1]$
= $64000[(\frac{43}{40})^3-1]$
= $64000 \times \frac{(43)^3-(40)^3}{64000}$
= $79507-64000=Rs.$ $15,507$
=> Ans – (C)
16) Answer (C)
17) Answer (C)
Principal amount = Rs. 10,000
Rate of interest = 10% for first year and 12% for second year
=> Amount after interest = $10,000 \times \frac{110}{100} \times \frac{112}{100}$
= $110 \times 112=Rs.$ $12,320$
=> Ans – (C)
18) Answer (B)
Principal (P) = Rs. 6250
Rate of interest (r) = 8% and time period (t) = 2 years
Simple interest = $\frac{P \times r \times t}{100}$
= $\frac{6250 \times 8 \times 2}{100}$
= $62.5 \times 16=Rs.$ $1000$
Compound interest = $P[(1+\frac{r}{100})^t-1]$
= $6250[(1+\frac{8}{100})^2-1]$
= $6250[(\frac{27}{25})^2-1]$
= $6250 \times (\frac{104}{625})$
= $Rs.$ $1040$
$\therefore$ C.I. – S.I. = $1040-1000=Rs.$ $40$
=> Ans – (B)
19) Answer (D)
Principal (P) = Rs. 5000
Rate of interest (r) = 8% and time period (t) = 2 years
Simple interest = $\frac{P \times r \times t}{100}$
= $\frac{5000 \times 8 \times 2}{100}$
= $50 \times 16=Rs.$ $800$
Compound interest = $P[(1+\frac{r}{100})^t-1]$
= $5000[(1+\frac{8}{100})^2-1]$
= $5000[(\frac{27}{25})^2-1]$
= $5000 \times (\frac{104}{625})$
= $Rs.$ $832$
$\therefore$ C.I. – S.I. = $832-800=Rs.$ $32$
=> Ans – (D)
20) Answer (D)
Rate of interest (r) = 4 % and time (t) = 2 years
Difference between simple and compound interests (d) = Rs. 1
Then, the sum = $\frac{d \times (100)^t}{(r)^t}$
= $\frac{1 \times (100)^2}{(4)^2} = \frac{10000}{16}$
= Rs. 625
=> Ans – (D)
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