On this page, you will read important chapters of Mathematics subject, definition of Compound Interest, formula, tricks and related questions and solutions etc.
In the previous post, we have shared the information about the Mathematics Formula and Simple Interest definitely read it.
Let us read and understand the information about compound interest.
Definition of Compound Interest
When we borrow money from a bank or a person, in return for using that borrowed money as per our wish, we give the amount of borrowed money and some extra money to the bank or person, this extra money is called interest.
The bank or the person from whom we borrow money is called the moneylender.
The money borrowed is called the principal.
The specified period for which the money is borrowed is called time.
The amount returned i.e. the combined form of principal and interest is called compound amount.
The amount of interest on any money depends on the principal amount, the period of time and the rate of interest.
The relationship between principal, period of time and rate of interest is as follows.
Interest = (Principal × Time × Rate)/100
The net worth at the end of the specified period is worked out as follows.
Compound Money = Principal + Interest
The amount of interest is paid immediately when interest is due, interest can be obtained by re-lending this interest amount or by investing it elsewhere.
By adding the interest thus obtained to the principal, a new principal is obtained, which can be re-lent or invested elsewhere.
In this way, this action can be repeated for many periods, the difference between the compound amount and the initial principal at the end of the last period is called Compound Interest, it is also called interest-by-interest.
Interest is usually given at the end of one year, six months or three months or at the end of three months, then we call it compounded annually, compounded half yearly or quarterly respectively.
Compound Interest Formula
- Compound Interest = (1 + Rate / 100 )^Time – Principal
- Compound Interest = Principal [(1 + Rate / 100)^times – 1]
- Compound Interest = Compound – Principal
The Mix is Calculated as Follows.
- Compound = Principal × (1 Rate / 100)^Time
- Compound = principal + interest
The points to be noted while calculating compound interest by the formula are –
If compound interest is compounded half-yearly, ie half-yearly, then the number of years is doubled and the annual rate of interest is halved.
Since one year = 2 × six months and the annual rate of interest is r, the half yearly rate r/2,
If the compound interest is compounded quarterly, that is, when the period of adding interest is quarterly, the number of years is quadrupled and the annual rate of interest is quartered.
Since 1 year = 4 × 3 months and the annual rate of interest is r, the quarterly rate = r/4.
Tricks to Calculate Compound Interest
Money = Difference × (100/rate)^time
Note : This Formula Will be Applicable Where the time is 2 years.
- A = P × 100 + % / 100 × 100 + % / 100 + ……………
- P = A × 100 + % / 100 × 100 / 100 + % + ……………
Note : To solve the questions on compound interest, below are the values of some numbers for 2 years and 3 years, so that you can solve the given questions easily.
| Compound Interest | Two Years | Three Year |
|---|---|---|
| 5% | 10.25% | 15.76% |
| 8% | 16.64% | 25.97% |
| 10% | 21% | 33.10% |
| 12% | 25.44% | 40.49% |
| 15% | 32.25% | 52.09% |
| 20% | 44% | 72.80% |
| 25% | 56.25% | 95.31% |
Examples of Compound Interest
Q.1 What will be the compound interest on Rs.8000 at the end of three years at the rate of 5 percent per annum?
A.1251
B.1378
C.1261
D.1876
Solution:- According to the question,
Compound Interest = Principal × [(1 + Rate / 100)^times – Principal]
= 8000 × (1 + 5/100)³ – 8000
= 8000 × 105/100 × 105/100 × 105/100 – 8000
= 9261 – 8000
= 1261
Ans. 1261
Q.2 A sum of Rs.12000 was lent at 8% for 2 years. What are the compound and compound amounts?
A.1398.89
B.2678.98
C.13996.80
D.1456.87
Solution:- According to the question,
Compound Interest = Principal × [(1 + Rate / 100)^time – Principal]
= 1200 × [(1 + 8 / 100)² – 1200]
= 1200 × [(27/25)² – 1200]
= 1200 × 27/25 × 27/25 – 1200
= 69,984/5
= 13,996.8
Ans. 13,996.8
Q.3 A sum of Rs.5,000 was lent at the rate of 12% for 2 years. Find the compound interest?
A.1278
B.1272
C.1378
D.1450
Solution:- According to the question,
Compound Interest = Principal × [(1 + Rate / 100)^time – Principal]
= 5000 × [(1 + 12/100)² – 5000]
= 1200 × [(28/25)² – 5000]
= 1200 × 28/25 × 28/25 – 5000
= 6,272 – 5000
= 1272
Ans. 1272
Q.4 50000 Rs. What will be the compound interest on an amount of 8% per annum for a period of 2 years?
A. 4000 Rs.
B. 8520 Rs.
C. 8000 Rs.
D. 8320 Rs.
Solution:- According to the question,
Compound Interest = Principal × [(1 + Rate / 100)^time – Principal]
= 50000[(1 + 8/100)² – 50000]
= 50000 [(27/25)² – 50000]
= [(50000 × 27/25 × 27/25) – 50000]
= 27 × 27 × 80
= 58,320 – 50000
= 8320 Rs.
Ans. 8320 Rs.
Q.5 Find the compound interest on Rs.800 at 5% per annum for 2 years?
A. Rs.80
B. 84 Rs.
C. Rs.82
D.88 Rs.
Solution:- According to the question,
Compound Interest = Principal × [(1 + Rate / 100)^time – Principal]
= 800[(1 + 5/100)² – 800]
= 800 [(21/20)² – 800]
= 800 × 21/20 × 21/20 – 800
= 882 – 800
= 82
Ans. 82
Q.6 800 Rs. What will be the compound interest at 6% per annum for 9 months approximately when the rate of interest is compounded quarterly?
A.36.40
B.36.50
C.36.65
D.36.60
Solution:- According to the question,
Quarterly rate of interest = 6/4
Compound Interest = Principal × [(1 + Rate / 100)^time – Principal]
= 800 [(1 + 6/4 × 100)³ – 800] Rs.
= 800 [(1 + 3/200)³ – 800]
= 800 [(203/200)³ – 800]
= 800 (203/200 × 203/200 × 203/200) – 800
= 800 (8365427 – 80000000)/80000000
= (800 × 365427)/80000000
= Rs 36.50 approx
Ans. 36.50
Q.7 Rs.4800 at 15% per annum. What will be the compound interest for two years on an amount of Rs.
A.1440
B.828
C.1484
D.1448
Solution:- According to the question,
Compound Interest = Principal × [(1 + Rate / 100)^time – Principal]
= 4800 [(1 + 15/100)² – 4800] Rs.
= 4800 [(23/20)² – 4800]
= 4800 × 23/20 × 23/20 – 4800
= 6,348 – 4800
= Rs 1,548
Ans. 1548 Rs.
Q.8 Rs.1000 at 15% per annum interest. What will be the compound interest in three years?
A.495.75
B.546.75
C.520.875
D.899.890
Solution:- According to the question,
Compound Interest = Principal × [(1 + Rate / 100)^time – Principal]
= 1000 [(1 + (15/100)³ – 1000] Rs.
= 1000 [(23/20)³ – 1000]
= 1000 × 23/20 × 23/20 × 23/20 – 1000
= 12167/8 – 1000
= 1520.875 – 1000
= 520.875
Ans. 520.875 Rs.
Q.9 16000 Rs. What will be the compound interest for two years at the rate of 20% per annum on an amount of Rs.
A.6070
B.7040
C.7060
D.4070
Solution:- According to the question,
Compound Interest = Principal × [(1 + Rate / 100)^time – Principal]
= 16000 [(1 + 20/100)² – 16000] Rs.
= 16000 [(6/5)² – 16000] Rs.
= 16000 × 6/5 × 6/5 – 16000
= 23040 – 16000
Ans. 7040
Q.10 7500 Rs. What will it become in 2 years at 4% per annum compound interest?
A.8082
B.8100
C.7800
D.8112
Solution:- According to the question,
Compound = Principal (1 + Rate/100)²
Amount = 7500 (1 + 4/100)²
Amount = 7500 (26/25)²
Amount = 7500 × 26/25 × 26/25
Mixed amount = Rs.8112.
Ans. 8112 Rs.
Q.11 A sum of Rs.400 is lent at compound interest for 3 years at 10%, 5%, and 20% per annum for the first, second, and third years respectively, then what will be the amount at the end of time to be returned?
A.345.0
B.189.0
C.310.0
D.554.4
Solution:- A = P × 100 + % / 100 × 100 + % / 100 + ……………
= 400 × 100 + 10 / 100 × 100 + 5 / 100 × 100 + 20 /100
= 400 × 110/100 × 105/100 × 120/100
= 400 × 11/10 × 21/20 × 6/5
= 4 × 11 × 21 × 6/5
= 11 × 12 × 21 / 5
= 132 × 21/5
= 2775/5
= 554.4
Ans. 554.4
Q.12 A sum of Rs 25000 is lent at compound interest for 4 years at 10% for the first 2 years 20% per annum for the last two years What will be the total amount returned at the end of time?
A. 12450
B. 16890
C. 18560
D. 20970
हल:- According to the question,
A = P × 100 + % / 100 × 100 + % / 100 + ……………
= 25000 × 100 + 10 / 100 × 100 + 10 / 100 × 100 + 20 /100 × 100 + 20/100
= 25000 × 110/100 × 110/100 × 120/100 × 120/100
= 30 × 121 × 12
= 360 × 121
= 43,560 – 25000
Ans. 18560
Q.13 An amount of Rs.50,000 at the rate of 2% per annum for the first year and 20% per annum for the next 2 years. What amount will be returned at the end of time?
A.23,440
B.24,890
C.25,890
D.26,980
Solution:- According to the question,
A = P × 100 + % / 100 × 100 + % / 100 + ……………
= 50,000 × 100 + 02 / 100 × 100 + 20 / 100 × 100 + 20 /100
= 50,000 × 102/100 × 120/100 × 120/100
= 5 × 102 × 12 × 12
= 510 × 144
= 23,440
Ans. 23,440
Q.14 A sum of Rs.12000 is lent for a total of 3 years at 25% per annum for the first two years and 40% per annum in the last year?
A.14,250
B.15,670
C.16,890
D.18,980
Solution:- According to the question,
A = P × 100 + % / 100 × 100 + % / 100 + ……………
= 12000 × 100 + 25 / 100 × 100 + 25 / 100 × 100 + 50 /100
= 12000 × 125/100 × 125/100 × 140/100
= 125 × 3 × 70
= 26,250 – 12000
= 14,250
Ans. 14,250
Q.15 A sum of money doubles itself in 5 years at compound interest per annum, how many times will it become in 15 years?
A.12 times
B. 14 times
C.16 times
D.20 times
in 5 years = 2 times
in 5 years = 4 times
in 5 years = 16 times
Will be 16 times in 15 years.
Ans. 16 times
Q.16 A sum of money doubles itself in 6 years at compound interest per annum, then in how many years will it become 32 times?
A.12 times
B. 14 times
C.16 times
D.20 times
in 6 years = 2 times
in 6 years = 4 times
in 6 years = 8 times
in 6 years = 16 times
in 6 years = 32 times
Total will become 32 times in 30 years.
Ans. 32 times
Q.17 A person borrowed some amount and returned it in two equal installments of 8,820 per annum. If the rate of compound interest is 5% per annum, then what is the amount borrowed?
A.16,400
B.8,900
C.3,890
D.7,890
Formula:- Principal % = Installment / (100 + % / 100)^1 + Installment / (100 + % / 100)²
Principal = 8,820/(100 + 5 /100) + 8,820/(100 + 5/100)
Principal = 8,820 / 105 / 100 + 8,820 / (105 / 100)²
Principal = 8,820 / 21 / 20 + 8,820 / (21 / 20)²
Principal = 8,820 / 21 / 20 + 8,820 / 441 / 400
Principal = 8,820 × 20 / 21 + 8,820 × 400 / 441
Principal = (8,400 + 8,000)
Principal = 16,400
Ans. 16,400
Q.18 A person borrowed Rs.19860 and the amount is to be paid in three equal instalments, what will be the amount of each instalment, if the rate of interest is 10% per annum?
A.6789
B.7986
C.9456
D.7895
Solution:- 19860 = x/100+10/100 + x/(100+10/100)² + x/(100+10/100)³
19860 = x /11/10 + x /(11/10)² + x /(11/10)³
19860 = x/11/10 + x/121/100 + x/1331/1000
19860 = 10x/11 + 100x/121 + 1000x/1331
19860 = 1210x + 1100x + 1000x / 1331
19860 × 1331 = 3310x
x = 19860 × 1331 / 3310
x = 7,986
Ans. 7,986
Q.19 A, B, and C invest sums in the ratio 3 : 4 : 5 respectively in schemes offering compound interest at the rate of 20% per annum, 15% per annum and 10% per annum respectively, after 1 year What will be the ratio of their amount?
A.6 : 5 : 8
B.5 : 9 : 4
C.6 : 6 : 5
D.2 : 6 : 8
Solution:- A : B : C
= 3 : 4 : 5
= 300 : 400 : 50
= 20% : 15% : 10%
= 20% of 300 : 15% of 400 : 10% of 500
= 300 × 20 / 100 : 400 × 15 / 100 : 500 × 10 / 100
= 60 : 60 : 50
= 6 : 6 : 5
Ans. 6 : 6 : 5
Q.20 A bank offers 5% interest compounded half yearly. A customer deposits Rs.8000 on 1st January and 1st July in 1 year. What amount will he gain by way of interest at the end of the year?
A.820
B.356
C.900
D.680
Solution:- 5% half yearly rate
End of 1 year = ?
1 Jan = 8000
1st July = 8000
= 8000/100 × 5
= 400
1st July = 8000 + 400 + 8000
= 16400/100 × 5
= 820
Ans. 820
Q.21 A sum of money becomes 4 times in 2 years and 9 times in 4 years, what is the rate of compound interest?
A.20
B.70
C.50
D.100
Solution:- 4 times in 2 years
9 times in 4 years
9/4 = (1 + r/100)²
√9/4 = 1 + r/100
3/2 = 1 + r/100
3/2 – 1 = r/100
1/2 = r/100
r = 50
r = 50
Ans. 50
Q.22 The difference between simple interest and compound interest on a sum of money at the rate of 5% in two years is Rs.25, what is that sum?
A.4890
B.5184
C.10,000
D.1,000
Solution: Money = Difference × (100/Rate)^Time
Note:- This formula will be applicable only where the time is 2 years.
Money = 25 × (100/5)²
= 25 × (20)²
= 25 × 20 × 20
Ans. 10,000
Q.23 A sum of Rs 7500 was borrowed at 4% per annum compound interest, how much amount will have to be returned after 2 years?
A.8112
B.9832
C.7895
D.5691
Solution:- Amount = Principal (1 + Rate/100)^Time
= 7500 × (1 + 4/100)²
= 7500 × (26/25)²
= 7500 × 26/125 × 26/25
Ans. 8112
Q.24 A sum of money becomes eight times of itself in 3 years at compound interest at what rate of interest?
A.100%
B.8%
C.1%
D.110%
Solution:- According to the question,
Let principal = p and
rate = r
8p = p(1 + r/100)³
8 = (1 + r/100)³
r = 100%
Ans. 100%
Q.25 A certain sum of money at compound interest amounts to Rs. 800 in 3 years. And Rs. 840 in 4 years. What is the percentage rate of interest?
A.5%
B.2%
C.4%
D.10%
Solution:- According to the question,
Let the amount be x Rs. Are.
The rate of interest is y percent.
800 = x (1 + y/100)³ ………(1)
840 = x (1 + y/100)⁴ …………(2)
Dividing (2) by (1)
840/800 = x (1 + y/100)⁴/x (1 + y/100)³
840/800 = 1 + y/100
840/800 – 1 = y/100
y/100 = 840/800 – 1
y/100 = (840 – 800)/800
y/100 = 40/800
y = 40/800 × 100
y = 5%
Ans. 5%
Q.26 The interest on a sum at 8% compound interest for the first year is Rs.48. Will the interest for the second year be?
A.48 Rs.
B. 51.84 Rs.
C. 56.48 Rs.
D.96 Rs.
Solution:- According to the question,
Principal = (48 × 100)/8
Principal = Rs.600.
Interest for 2nd year = 8% of 648
= 648 × 8/100
= 51.84
Ans. 51.84
FAQ
Ans. Compound interest is when you earn interest on the money you’ve saved and on the interest you earn along the way.
Ans. In simple terms, compound interest can be defined as interest you earn on interest.
Ans. To calculate interest rates, use the formula : Interest = Principal × Rate × Tenure.
Ans. Time = Distance ÷ Speed.
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