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Simple Interest and Compound Interest Shortcuts With Examples

Simple Interest and Compound Interest Shortcuts With Examples





Hard Work along with smart work makes you perfect to win in competitive exams. In every competitive exam, there is a time constraint for up calculations that time management plays a crucial role so learn some shortcut tricks in every concept of quantitative laptop calculations these problems in the main exam. Here, we have updated some compound interest and simple interest shortcut tricks with examples. these problems you can save time in competitive exams.

For better understanding, watch the video on simple interest and compound interest shortcuts.

Compound Interest Shortcut Tricks with Examples

Simple Interest Shortcut Tricks with Examples




Compound Interest Practice Problems for IBPS Bank Exams

These are the different type of questions asked on compound interest under quantitative aptitude section. Here are some of the practice .problems on compound interest for bank exams collected from previous years bank exams.

1.What will be the compound Interest on a sum of Rs.7500 at 4% per anum in 2 years?
(a) Rs.618
(b) Rs.612
(c) Rs.624
(d) Rs.606
(e) Rs.621

Solution: CI % for 2 years = 4 + 4 + 16/100 = 8.16%
100% =7500
Then, 8.16% = ?
By cross multiplication,
CI = 8.16 * 7500/100 = 612.

2. What would be the compound interest accrued on an amount of Rs.10,000 at the rate of 20% in 2 years? If the interest is compounded half yearly?

Explanation:
StepI:
Here Rate = 20% per anum
Convert Rate% per half year = 10%.

Step II:
Time = 4 half years.
CI for first 2 half years = 10 + 10 + 100/100 = 21
CI for 3rd half year = 10 + 21 + 210/100 = 33.1
CI for 4th half year = 10 + 33.1 + 331/100 = 46.41
P (100%) = 10000
CI for 4 half years i.e. 46.41% = ?
By cross multiply,
CI = 46.41 * 10000/100 = 4641

3. How much will a sum of Rs.6300 amount to in a span of 2 years at 5% per anum rate of compound interest?
(a) Rs. 6946
(b) Rs. 6876
(c) Rs. 6521
(d) Rs. 6790
(e) Rs. 6492

Solution:
Always assume the principle amount (P) as 100%
Here P = 100%= 6300
CI % for 2 years = 5 + 5 + 25/100 = 10.25%

Amount = Principle + Interest = 100 + 10.25 = 110.25%

From the problem, 100% = 6300
Then Find Amount i.e. 110.25% = ?
By cross multiplication,
CI = 110.25 * 6300/100 = 6946 (approx).

4. How much will be the compound interest to be paid on a principle amount Rs.85000 after 3 years at the rate of 6% per anum?
(a) Rs. 16623.36
(b) Rs. 16236.36
(c) Rs. 16326.36
(d) Rs. 16632.36
(e) Rs. 16263.36

Solution:
Step 1: CI Rate for First 2 years = 6 + 6 + 36/100 = 12.36% (Formula for Net Percentage= a + b + ab/100)
Step 2: CI Rate for the 3rd year = 6 + 12.36 + 74.16/100 = 19.10%

The CI Rate for 3 years = 19.1%, Principle = Rs.85000 (Assume 100%)

Then, 100% = 85000
19.1% = ?
By cross multiplication,
Compound Interest for 3 years = 19.1 * 85000/100 = Rs. 16236.36

5. How much will be the compound interest to be paid on a principal amount of Rs.53,000 after 2years at the rate of 4% per anum?
(a) Rs. 4324.8
(b) Rs. 4432.8
(c) Rs. 4342.8
(d) Rs. 4234.8




Solution: CI % for 2 years = 4 + 4 + 16/100 = 8.16%
100% = 53,000
Then, 8.16% = ?
By cross multiplication,
CI = 8.16 * 53000/100 = 4342.8

6. What appropriate amount of compound interest can be obtained in an amount of Rs.9650 at the rate of 6 percent per anum at the end of 3 years?
(a) Rs. 1737
(b) Rs. 1920
(c) Rs. 1720
(d) Rs. 1860
(e) Rs. 1843

Solution:

CI for 3 years = First 2 years + the 3rd year.
For 2 years = 6 + 6+36/100 =12.36
For 3rd year = 6 + 12.36 + 74.16/100 = 18.36 + 0.74 = 19.1%

Therefore, If 100% = 9650 ( principal given).
Then find CI 19.1% =?
By cross multiplication, The compound interest for 3 years
19.1 * 9650/100 = 1843.

7. What is the compound interest accrued on an amount of Rs.25,000 in two years @12 percent per anum?
(a) 6630
(b) 6360
(c) 6260
(d) 6460
(e) None of these.

Solution:
CI for 2 years = 12 + 12 + 144/100 = 25.44
100% = 25000
25.44% = ?

=> 25.44 * 25000/100 = 6360.
8. What is the compound interest accrued on an amount of Rs.12,000 at the rate of 10% at the end of 3 years?
(a) Rs.3972
(b) Rs.2567
(c) Rs.4780
(d) Rs.4780
(e) Rs.5609

CI For first 2 years = 10 + 10 + 100/100 (a + b + ab/100).
= 21
CI For 3rd year = 10 + 21 + 210/100 = 33.1

Then 33.1% =?
If 100% = 12000
By cross multiply,
CI For 3 years (33.1%) = 33.1 * 12000/100 = 331* 12 = 3972.

9. The compound interest accrued on an amount at the end of two years at the rate of 12% is Rs.2862. What is the amount?
(a) 11250
(b) 12200
(c) 13500
(d) 10000

Solution: CI for 2 years = 12 + 12 + 144/100 = 25.44% = Rs. 2862 (given)
P = 100% = ?

By cross multiply,P = 100 * 2862/25.44 = 11250.

10. The compound Interest earned on a sum in 3 years at 15% per anum compounded annually is Rs.6500.52. What is the sum?
(a) Rs. 12480
(b) Rs. 10500
(c) Rs. 14800
(d) Rs. 13620

Solution: CI for first 2 years = 15 +15 +225/100 = 32.25
CI for 3rd year = 15 + 32.25 + 483.75/100 = 47.25 + 4.84 = 52.09%
Here the compound interest for 3 years (52.09%) = 6500.52
Then Principle Amount (100%) = ?
By cross multiply,
= 100 * 6500.52/52.09 = 12480.

11. The Difference between the compound interest and simple interest accrued on an amount of Rs.26000 at the end of 3 years is 2994.134 . What is the rate of interest p.c.p.a?
(a) 22
(b) 17
(c) 19
(d) Cannot be determined
(e) None of these

Solution :

Note: difference between simple interest and compound interest shortcut formula
Method I: ofWhen the difference between CI and SI for 3 years (D) is given,
The Principle = Difference * 100^3 / [r^2 ( r +300)]

Substitute the given values in above formula to get Rate%.

P= 26000, d =2994.134
26000 = 2994134000/[r^2 ( r +300)]=> [r^2 ( r +300)] = 2994134000/26000
=> [r^2 ( r +300)] = 115159
Substitute r value from the given options to get quick answer.
=> 19^2 (19 +300) = 115159
Therefore r = 19.

12. Sudharshan invested Rs.15000 at interest @10% per anum for one year. If the interest is compounded every six months what amount will Sudarshan get at the end of the year?
(a) 16537.50
(b) 16500
(c) 16525.50
(d) 18150

Explaination:
P (100%) = 15000, Rate = 10% per anum (convert this for half year = 5%)

Time = 2 half years
CI for 2 half years = 5 + 5 + 25/100 = 10.25% (CI for 1 year compounded half yearly)
Amount = P + CI = 100 + 10.25 = 110.25%
Here P is 100% = 15000
Find Amount, 110.25% = ?

Amount = 110.25 * 15000/100 = 16537.50

Simple Interest Shortcut Tricks With Examples

13) In how many years will Rs.4600 amount to Rs.5428 at 3% per anum at Simple interest?
(a) 3
(b) 5
(c) 6
(d) 4
(e) none of these.

Solution:
(Short trick: Assume Principle amount = 100% and Simple Interest = (Time * Rate))

Principle amount (sum) = 100% = 4600 (given)
Interest = 3% *(x years) = 5428 – 4600 = 828

By cross multiplication,
3x = 828 * 100/ 4600
x= 18/3 => 6 years.
14) The simple interest accrued on a sum of certain principle is Rs.1200 in 4 years at the rate of 8% per anum. What would be the simple interest accrued on thrice of that principle(P) at the rate of 6% per anum in 3 years?
(a) 2025
(b) 3025
(c) 2250
(d) 2150

Solution:

Step I: SI for 4 years at 8%p.a. = 4*8 =32% = 1200(SI given in problem)

Here, SI (32%) = 1200
P = (100%) = ?
=> P= 100 * 1200/32= 3750

Step II:
New Principle = 3750 * 3 = 11250, SI for 3 years at 6% rate = 18%

New P (100%) = 11250,
New SI 18% = ?
=> 18 * 11250/100 = 2025.

15) At what rate of simple interest will Rs.4800 amount to Rs.6480 in a span of 7 years?

Solution:
(Short trick: Assume Principle amount = 100% and Simple Interest = (Time * Rate))

100% = 4800
(7 * x%) = 6480 -4800 = 1680

By cross multiplication,

Rate (x%) = (1680 * 100)/ 4800 * 7
= 5%.

16) Mr.Khan took a loan of Rs. 10,000 on simple interest for 2 years at the rate of 3% per anum. The total amount that he will be paying as interest in 2 years is 3% of his monthly salary. What is his monthly salary?

(a) Rs.30,000
(b) Rs.16,000
(c) Rs.20,000
(d) Rs.12,000
(e) Rs. 15,000

Explanation:

Step I: Calculate SI for 2 years on sum of Rs.10,000 using Simple Interest Shortcut Trick

100% = 10,000
6% = ?
By cross multiplication, The Simple Interest is

6 * 10000/100 = Rs. 600.

Step II:
From the problem, 3% = Rs.600
Then Find, 10=?
Monthly Salary (100%) = 100 * 600/3 = Rs. 20,000.
Note: If you practice some problems using this Simple Interest Shortcut trick, we can solve in quick time than usual methods. Here for the understanding purpose explained step by step method but in exams do calculations mentally.

17) Simple Interest accrued on an amount in eight years @11 percent per anum is Rs.57,200. What was the principal amount?
(a) Rs.72,000
(b) Rs.82,000
(c) Rs.75,000
(d) Rs.65,000
(e) None of these.

Solution:
Always Principal(P) amount is 100%
From the problem, SI for 8 years @11 = 8* 11 = 88%
Here 88% = 57200
Then find 100% =?
By cross multiplication,
Principal (100%) = 100*57200/88 = 65000

18) The amount of simple interest accrued on an amount of Rs. 28,500 in seven years is Rs. 23,940 . What is the rate of interest p.c.p.a?
(a) 10.5
(b) 12.5
(c) 11
(d) 12

Solution: 100% =28500,
SI (7 years * x%) = 28500 – 23940 = 4560
=> 7x% (Rate)= 4560*100/28500
=>7 = 4560/285*7 = 12

19) What is the difference between the simple interest and compound interest on Rs. 7300 at the rate of 6% in 2 years?
(a) 29.37
(b) 26.28
(c) 25.34
(d) 26.45
(e) 21.34

Solution: (We can solve this problem by using the percentage shortcut trick used in above problems or can solve by using formula i.e

Shortcut method:
SI% for 2 years = (Time * Rate) = 2* 6 = 12%
CI% for 2 years = 6 + 6 + 36/100 =12.36%
DIfferce of CI and SI = 12.36% -12% = 0.36%
Always we know the Principle = 100%
Here P (100%) = 7300
Then 0.36% = ?
By cross multiplication,
Difference of CI and SI (0.36%) = 0.36 * 7300/100 = 26.28

20) Difference between the compound interest and simple interest accrued in two years at 8% per anum is Rs.128. What is the principal amount?
(a) 18000
(b) 16000
(c) 20000
(d) cannot be determined
(e) None of these

Solution:
Principal = d * 100^2 / r^2 (d =difference, r= rate)
=> 128 (10000/64)
=> 128 (2500/16)
=> 20000

21) The simple interest accrued on an amount of Rs.22500 at the end of four years is Rs.10,800. What would be the compound interest earned on the same amount at the same rate at the end of 2 years?
(a) 14908
(b) 8568
(c) 26234
(d) 5724

Solution: SI for 4 years at X% rate = 4X% = 10,800
100% = 22500
By cross multiplication solve X value,
=> 4X = 100 * 10800/22500
=>(Rate) X = 10800/(225*4) = 12%

Compound Interest for 2 years at 12% on 22500 = 12+ 12 + 144/100 = 25.44%
100% = 22500
25.44% = ?

By cross multiplication,
CI for 2 years (25.44%) = 25.44 * 22500/100 = 5724

Simple Interest and Compound Interest Practice Problems:

22) What amount would a man have received on a principle of Rs.4000 after 2 years at simple interest at the rate of 5% per annum?
(a) 4161
(b) 5200
(c) 4400
(d) 4100
(e) 4190

23) What total amount would Rajesh get at the end of 3 years? If he invests an amount of Rs.11,200 in a scheme which offers simple interest at the rate of 8.5% for 3 years? (Hint find Total Amount = P + SI)
(a) 14056
(b) 14354
(c) 13852
(d) 15065
(e) 16578

24) The simple interest accrued on an amount of Rs.40,000 at the end of three years is Rs.12000. What would be the compound interest accrued on the same amount at the same rate in the same period?
(a) 18765
(b) 15350
(c) 21555
(d) 13240

25) What would be the compound interest accrued on an amount of Rs? 45,400 at the end of two years at the rate of 15% per anum?
(a) Rs.16411.5
(b) Rs.14461.5
(c) Rs.16461.5
(d) Rs.14641.5
(e) Rs.15674.5

26) The simple interest accrued on the sum of certain principal is Rs.6500 in 8 years at the rate of 13% per year. What would be the compound interest accrued on that principal at the rate of 8% per year in two years?
(a) 1040
(b) 1020
(c) 1060
(d) 1200

Model II: Data Sufficiency Questions on Compound Interest:

Directions: Each of the following questions consists of a question followed by 3 statements I, II and III. You have to study the question and the statements and decide which of the statement is necessary to answer the question.

1) Manjusha borrowed a sum at compound interest. What is the amount returned in 2 years?
I. The rate of interest is 5% per annum.
II. The simple interest incurred on the sum in 1 year is Rs.600.
III. The borrowed sum is ten times the amount earned as a simple interest in two years.
(a) Only I
(b) Only III
(c) Both II and III
(d) Either I or III
(e) All I, II and III.

2) What is the rate of interest percent p.a.?
I. Simple Interest earned per annum is Rs.5300
II. The difference between the compound interest and simple interest on an amount is Rs.1060 at the end of 2 years.
III. An amount doubles itself in 5 years with simple interest.

(a) Only I
(b) Only III
(c) Both II and III
(d) Either I or III
(e) All I, II and III.

3) What is the simple interest accrued on a principal of Rs.5000 in 6 years?
I. The rate of simple interest for the first 3 years is 5% per anum.
II. The rate of simple interest for the next three years is 8%.

Answer: Both I and II

3) What will be the amount at the end of 2 years? If the interest is compounded yearly.
(a) The simple interest on the same sum for a period of 2 years is Rs.400 at the same rate of 5% per anum.
(b) The difference between the simple interest and the compound interest for 2 years at the rate of 5% per anum is Rs.100.

Answer: Both (a) and (b)
From (a), we can find the Principal amount.

4) Mr. X borrowed a sum of money on compound interest. What will be the amount to be repaid if he is paying the entire amount at the end of two years?
(A) The rate of interest is 5% per anum
(B) Simple interest fetched on the same amount in one year is Rs.600.
(C) The amount borrowed is 10 times the simple interest in two years.

(1) C only
(2) A only
(3) An or B Only
(4) An or C only
(5) All A, B, and C are required to answer the question.


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