Compound Interest Questions and Answers

Q: The rate percent per annum compound interest, where ₹5,000 amounts to ₹5,832 in two years, will be

The rate is 8% per annum.For compound interest compounded annually, \(A = P(1 + r)^{2}\):\[ \begin{aligned} (1 + r)^{2} &= \frac{5832}{5000} = 1.1664 \\ 1 + r &= 1.08 \\ r &= 8\% \end{aligned} \]Check: 5000 × 1.08 = 5400 after one year, and 5400 × 1.08 = 5832 after two. At 10% the amount would be 6050, and at 5% or 7% it would be 5512.50 or 5724.50.

Q: A papaya tree was planted two years ago. It grows at the rate of 20 % every year. If at present height of tree is 540 cm, when it was planted, what was its height

The tree was 375 cm tall when planted.Growing by 20% a year for two years multiplies the height by \(1.2^{2} = 1.44\), so\[ h = \frac{540}{1.44} = 375\ \text{cm} \]Check: 375 rises to 450 after one year and to 540 after two. 324 cm comes from removing 40% of 540, two 20% cuts added together; undoing a rise needs division by 1.2 for each year, not a 20% cut. 432 cm is 540 less a single 20%, and 324 mm changes the unit.

Q: On a certain sum, the difference between compound interest and simple interest at 10% p.a. for 2 years is ₹ 126. Find the sum. (in ₹).

The sum is ₹ 12,600.For 2 years, the difference between compound and simple interest is the interest on the first year's interest:\[ \begin{aligned} CI - SI &= P \left(\tfrac{R}{100}\right)^{2} \\ 126 &= P \times 0.01 \\ P &= 12600 \end{aligned} \]Check: on ₹ 12,600 at 10%, simple interest for 2 years is ₹ 2,520 and compound interest is ₹ 2,646, a difference of ₹ 126.

Q: Find the compound interest on Rs. 31,250 at 8% p.a for 3 years compounded annually?

The compound interest is Rs. 8116.\[ \begin{aligned} A &= 31250 \times \left(\frac{27}{25}\right)^{3} \\ &= 31250 \times \frac{19683}{15625} \\ &= 2 \times 19683 = 39366 \end{aligned} \]CI = 39366 - 31250 = 8116.Year by year: 2500 in the first year, 2700 in the second and 2916 in the third, which also total 8116. Simple interest for 3 years would be 7500; the other options are near misses from rounding.

Q: A sum of money tripled itself at compound interest in 10 years. In how many years will it become 27 times ?

It will take 30 years.At compound interest the money is multiplied by the same factor in every equal period. It triples in 10 years, so:\[ 27 = 3 \times 3 \times 3 \]Three tripling periods of 10 years make 30 years. 35, 31 and 32 years are not a whole number of 10-year tripling periods, so they cannot give exactly 27 times.

Q: If the compound interest on a certain sum for 2 years is Rs. 308 and the simple interest at same rate of interest and for same time is Rs. 280. Find the sum ?

The sum is Rs. 700.Simple interest for 2 years is 280, so 140 a year. The extra Rs. 28 in compound interest is interest on the first year's interest, so the rate is \(28/140 = 20\%\).\[ \begin{aligned} r &= \frac{28}{140} \times 100 = 20\% \\ P &= \frac{140 \times 100}{20} = 700 \end{aligned} \]Check: compound interest at 20% on 700 is \(700 \times 1.44 - 700 = 308\).

Q: In what time will Rs. 1,000 amount to Rs. 1,331 at 10% per annum, compounded annually ?

The time is 3 years.Under compound interest, \(A = P\left(1 + \frac{R}{100}\right)^{n}\).\[ \begin{aligned} 1000 \times (1.1)^{n} &= 1331 \\ (1.1)^{n} &= 1.331 = (1.1)^{3} \\ n &= 3 \end{aligned} \]Year by year: 1000 grows to 1100, then 1210, then 1331. Four years would give 1464.10 and five years 1610.51.

Q: The compound interest on ₹ 2,000 at 10% per annum for 2 years is

The compound interest is ₹ 420.Find the amount after 2 years, then subtract the principal:\[ \begin{aligned} A &= 2000 \left(1 + \frac{10}{100}\right)^{2} \\ &= 2000 \times 1.21 = 2420 \\ CI &= 2420 - 2000 = 420 \end{aligned} \]Check year by year: the first year earns ₹ 200, and the second year earns 10% of ₹ 2,200, which is ₹ 220, for a total of ₹ 420.₹ 400 is the simple interest for the same period, and ₹ 200 is only one year's interest.

Q: The difference between compound interest and simple interest on Rs. 700 in 2 years at 5% per annum is

The difference is Rs. 1.75.For 2 years, compound interest exceeds simple interest only by the interest earned on the first year's interest. The shortcut formula is:\[ \begin{aligned} CI - SI &= P\left(\frac{r}{100}\right)^{2} \\ &= 700 \times \left(\frac{5}{100}\right)^{2} \\ &= \frac{700}{400} = 1.75 \end{aligned} \]Check: the first year's interest is Rs. 35, and 5% of Rs. 35 is Rs. 1.75. Simple interest for 2 years is Rs. 70 and compound interest Rs. 71.75.Rs. 5 and Rs. 10 are far too large for a difference on Rs. 700 at 5%, and since Rs. 1.75 is offered, 'None of these' is wrong.

Important Instructions

21.

The rate percent per annum compound interest, where ₹5,000 amounts to ₹5,832 in two years, will be

A.5%
B.7%
C.10%
D.8%

Exam Year(s)

MPPSC Forest Service - 2023,

Answer: D

The rate is 8% per annum.

For compound interest compounded annually, \(A = P(1 + r)^{2}\):

\[ \begin{aligned} (1 + r)^{2} &= \frac{5832}{5000} = 1.1664 \\ 1 + r &= 1.08 \\ r &= 8\% \end{aligned} \]

Check: 5000 × 1.08 = 5400 after one year, and 5400 × 1.08 = 5832 after two. At 10% the amount would be 6050, and at 5% or 7% it would be 5512.50 or 5724.50.

Discuss in Forum

22.

A papaya tree was planted two years ago. It grows at the rate of 20 % every year. If at present height of tree is 540 cm, when it was planted, what was its height

A.324 cm
B.375 cm
C.432 cm
D.324 mm

Exam Year(s)

Northern Coalfields Limited - 2020, NCL Technician - 2020,

Answer: B

The tree was 375 cm tall when planted.

Growing by 20% a year for two years multiplies the height by \(1.2^{2} = 1.44\), so

\[ h = \frac{540}{1.44} = 375\ \text{cm} \]

Check: 375 rises to 450 after one year and to 540 after two. 324 cm comes from removing 40% of 540, two 20% cuts added together; undoing a rise needs division by 1.2 for each year, not a 20% cut. 432 cm is 540 less a single 20%, and 324 mm changes the unit.

Discuss in Forum

23.

On a certain sum, the difference between compound interest and simple interest at 10% p.a. for 2 years is ₹ 126. Find the sum. (in ₹).

A.₹ 12,000
B.₹ 12,600
C.₹ 16,200
D.₹ 10,800

Exam Year(s)

RSMSSB - 2024, RSMSSB Mahila Supervisor - 2024,

Answer: B

The sum is ₹ 12,600.

For 2 years, the difference between compound and simple interest is the interest on the first year's interest:

\[ \begin{aligned} CI - SI &= P \left(\tfrac{R}{100}\right)^{2} \\ 126 &= P \times 0.01 \\ P &= 12600 \end{aligned} \]

Check: on ₹ 12,600 at 10%, simple interest for 2 years is ₹ 2,520 and compound interest is ₹ 2,646, a difference of ₹ 126.

Discuss in Forum

24.

Find the compound interest on Rs. 31,250 at 8% p.a for 3 years compounded annually?

A.Rs. 8006
B.Rs. 8106
C.Rs. 8096
D.Rs. 8116

Exam Year(s)

TNPSC Group 1 - 2017, TNPSC - 2017,

Answer: D

The compound interest is Rs. 8116.

\[ \begin{aligned} A &= 31250 \times \left(\frac{27}{25}\right)^{3} \\ &= 31250 \times \frac{19683}{15625} \\ &= 2 \times 19683 = 39366 \end{aligned} \]

CI = 39366 - 31250 = 8116.

Year by year: 2500 in the first year, 2700 in the second and 2916 in the third, which also total 8116. Simple interest for 3 years would be 7500; the other options are near misses from rounding.

Discuss in Forum

25.

If the difference between S.I and C.I for 3 years at 5% is Rs. 183, then find the principal

A.18,000
B.8,000
C.24,000
D.30,000

Exam Year(s)

TNPSC Group 1 - 2025, TNPSC - 2025,

Answer: C

For 3 years the difference between compound and simple interest is:

\[P(\tfrac{r}{100})^{2}(3+\tfrac{r}{100})\]

With r = 5 this is:

\[P\times0.0025\times3.05=0.007625P=183\]\[P=\tfrac{183}{0.007625}=24000\]

So the principal is Rs 24,000, option C.

The difference between compound and simple interest for three years is given by the formula above, so the principal can be found by dividing 183 by the factor 0.007625.

Discuss in Forum

26.

A sum of money tripled itself at compound interest in 10 years. In how many years will it become 27 times ?

A.35 years
B.31 years
C.30 years
D.32 years

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: C

It will take 30 years.

At compound interest the money is multiplied by the same factor in every equal period. It triples in 10 years, so:

\[ 27 = 3 \times 3 \times 3 \]

Three tripling periods of 10 years make 30 years. 35, 31 and 32 years are not a whole number of 10-year tripling periods, so they cannot give exactly 27 times.

Discuss in Forum

27.

If the compound interest on a certain sum for 2 years is Rs. 308 and the simple interest at same rate of interest and for same time is Rs. 280. Find the sum ?

A.Rs. 700
B.Rs. 1200
C.Rs. 1100
D.Rs. 500

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: A

The sum is Rs. 700.

Simple interest for 2 years is 280, so 140 a year. The extra Rs. 28 in compound interest is interest on the first year's interest, so the rate is \(28/140 = 20\%\).

\[ \begin{aligned} r &= \frac{28}{140} \times 100 = 20\% \\ P &= \frac{140 \times 100}{20} = 700 \end{aligned} \]

Check: compound interest at 20% on 700 is \(700 \times 1.44 - 700 = 308\).

Discuss in Forum

28.

In what time will Rs. 1,000 amount to Rs. 1,331 at 10% per annum, compounded annually ?

A.5 years
B.3 years
C.6 years
D.4 years

Exam Year(s)

Tripura Public Service Commission - 2019,

Answer: B

The time is 3 years.

Under compound interest, \(A = P\left(1 + \frac{R}{100}\right)^{n}\).

\[ \begin{aligned} 1000 \times (1.1)^{n} &= 1331 \\ (1.1)^{n} &= 1.331 = (1.1)^{3} \\ n &= 3 \end{aligned} \]

Year by year: 1000 grows to 1100, then 1210, then 1331. Four years would give 1464.10 and five years 1610.51.

Discuss in Forum

29.

The compound interest on ₹ 2,000 at 10% per annum for 2 years is

A.₹ 200
B.₹ 400
C.₹ 420
D.₹ 440

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: C

The compound interest is ₹ 420.

Find the amount after 2 years, then subtract the principal:

\[ \begin{aligned} A &= 2000 \left(1 + \frac{10}{100}\right)^{2} \\ &= 2000 \times 1.21 = 2420 \\ CI &= 2420 - 2000 = 420 \end{aligned} \]

Check year by year: the first year earns ₹ 200, and the second year earns 10% of ₹ 2,200, which is ₹ 220, for a total of ₹ 420.

₹ 400 is the simple interest for the same period, and ₹ 200 is only one year's interest.

Discuss in Forum

30.

The difference between compound interest and simple interest on Rs. 700 in 2 years at 5% per annum is

A.Rs. 10
B.Rs. 5
C.Rs. 1.75
D.None of these

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: C

The difference is Rs. 1.75.

For 2 years, compound interest exceeds simple interest only by the interest earned on the first year's interest. The shortcut formula is:

\[ \begin{aligned} CI - SI &= P\left(\frac{r}{100}\right)^{2} \\ &= 700 \times \left(\frac{5}{100}\right)^{2} \\ &= \frac{700}{400} = 1.75 \end{aligned} \]

Check: the first year's interest is Rs. 35, and 5% of Rs. 35 is Rs. 1.75. Simple interest for 2 years is Rs. 70 and compound interest Rs. 71.75.

Rs. 5 and Rs. 10 are far too large for a difference on Rs. 700 at 5%, and since Rs. 1.75 is offered, 'None of these' is wrong.

Discuss in Forum

Loading…

Topics

Other Subjects

Tags: Compound Interest Questions and Answers || Compound Interest MCQ Questions and Answers || Compound Interest GK Questions and Answers || Compound Interest GK MCQ Questions || Compound Interest Multiple Choice Questions and Answers || Compound Interest GK || GK on Compound Interest || Quantitative Aptitude Questions and Answers || Quantitative Aptitude MCQ Questions and Answers || Quantitative Aptitude GK Questions and Answers || GK on Quantitative Aptitude

Compound Interest Questions and Answers

Important Instructions

Topics

Other Subjects

About Us

Stay informed about all important Dates & Notifications