Compound Interest is an important topic asked under the Arithmetic section in Mathematics. It is asked in various Defence Exams such as CDS, AFCAT, Air Force Group X & Y etc
We will discuss the basic questions that are usually asked in this topic and how you can solve them using the normal as well as Shortcut approach.
Tips & tricks on Compound Interest
Now, Let’s discuss the basic difference between Simple Interest and Compound Interest.
Principal = 1000, rate of interest (r) = 10%, time = 3yrs
Simple Interest
SI for 1^{st} yr = (1000×10×1)/100 = 100,
SI for 2^{nd} yr = 100 (In SI it will be the same as 1^{st} yr)
SI for 3^{rd} yr = 100
Compound Interest:
CI for 1^{st} yr = 100
CI for 2^{nd} yr will not be same as 1^{st} yr because principal for 2^{nd} yr is the amount of 1^{st} yr.
So, CI (2^{nd} yr) = (1100×10×1)/100 = 110
CI for 3^{rd} yr will also not be the same as 1^{st} yr and 2^{nd} yr because principal for 3^{rd} yr is the amount of 2^{nd} yr.
principal (3^{rd} yr) = Amount (2^{nd} yr) = Principal(2^{nd} yr)+Interest(2^{nd} yr) = 1100+110 = 1210
CI (3^{rd} yr) = (1210×10×1)/100 = 121
Hence total CI for 3yrs = 100+110+121 = 331
Amount after 3 yrs = 1331
Interest is always calculated on the Principal. But in the case of CI, the Principal is get changed every year.
Also Check: Tips & Tricks on Simple Interest
If we calculate it by net rate concept then the Principal will remain the same.
Concept1: How to calculate net CI rate for 2 years?
Let rate is r% per annum for 2 years
Net CI rate for 2yrs can be calculated by = 2r+(r^{2}/100)
If rate is 1%, net CI rate for 2yrs = 2×1+(1^{2}/100) = 2.01%
If rate is 3%, net CI rate for 2yrs = 2×3+(3^{2}/100) = 6.09%
If rate is 14%, net CI rate for 2yrs = 2×14+(14^{2}/100) = 29.96%
We suggest you to learn the table given below:
% Rate per annum | Net CI rate for 2 yrs | % Rate per annum | Net CI rate for 2 yrs |
2% | 4.04% | 9% | 18.81% |
3% | 6.09% | 10% | 21% |
4% | 8.16% | 11% | 23.21% |
5% | 10.25% | 12% | 25.44% |
6% | 12.36% | 13% | 27.69% |
7% | 14.49% | 14% | 29.96% |
8% | 16.64% | 15% | 32.25% |
Concept2: How to calculate net CI rate for 3 years?
Let rate is r% per annum for 3 years
Net CI rate for 3yrs can be calculated = 3r+3(r^{2}/100)+1(r^{3}/10000)
If rate is 3% p.a., net CI rate for 3 yrs
= 3×3+3(9/100)+1(27/10000)
= 9+.27+.0027 = 9.2727
If rate is 12% p.a., net CI rate for 3 yrs
= 3×12+3(144/100)+1(1728/10000)
= 36+4.32+.1728
= 40.4928
Representation while calculating net rate %.
Let’s calculate it for the rate 3% p.a.
write, r/r^{2}/r^{3} = 3/9/27
then,3r/3r^{2}/1r^{3} = 9/27/27
= 9.2727
We suggest you learn the table given below:
% Rate per annum | Net CI rate for 3 yrs | % Rate per annum | Net CI rate for 3 yrs |
1% | 3.31% | 6% | 19.1016% |
2% | 6.1208% | 7% | 22.5043% |
3% | 9.2727% | 8% | 25.9712% |
4% | 12.4864% | 9% | 29.5029% |
5% | 15.7625% | 10% | 33.10% |
Concept3: If the r% p.a. is in fraction:
Example: if rate is 16(2/3) % and principal is 216, then calculate CI for 2yrs and 3yrs.
Solution: We can write 16(2/3)% = 1/6 (Discussed in percentage study notes)
For 2 years
216×(1/6)= 36, Now multiply 36 by 2 = 72
36× (1/6) = 6 , multiply 6 by 1 = 6
Add both the above value = 72+6 = 78
CI for 2yrs = 78
For 3 years
216×(1/6) = 36, Now multiply 36 by 3 = 108
36× (1/6) = 6, multiply 6 by 3 = 18
6× (1/6) = 1, multiply 1 by 1 = 1
Add all the above values = (108+18+1)= 127
CI for 3yrs = 127
Concept4: When r% is given p.a. and CI has to be calculated half-yearly or quarterly basis.
Yearly | factor | r% (per annum) | Time (n yrs) |
Half yearly | 6months = (6/12) =1/2 | Factor× r% = (r/2) % | 2n |
Quarterly | 3months= (3/12) =1/4 | (1/4) × r% = (r/4) % | 4n |
9 months | 9months= (9/12) = 3/4 | (3/4) × r% = (3r/4) % | 4n/3 |
8 months | 8months= (8/12) = 2/3 | (2/3) × r% = (2r/3) % | 3n/2 |
Example: If r% = 10% per annum. Find the CI on 5000 for 2 years if it is compounded half-yearly.
Solution: Rate is calculated half yearly so new r% = (10/2)% = 5%
Given time is 2 yrs, acc.to half yearly, it will be 2×2 = 4
Now we have to calculate CI for 4yrs @ 5%
We know 5% = (1/20)
So, 5000×(1/20) = 250, multiply 250 by 4 = 1000
250× (1/20) = 12.5, multiply 12.5 by 6 = 75
12.5× (1/20) = 0.625, multiply 0.625 by 4 = 2.5
0.625× (1/20)= .03125 multiply .03125 by 1 = .03125
Add all the above values
(1000+75+2.5+0.03125)
= 1077.53125
Concept5: When different rates are given for 2 years.
If a% is given for 1^{st} year and b% is given for 2^{nd} year.
Net rate of CI for 2 yrs = (a+b+ab/100) % (discussed in percentage study notes)
Note: The net CI rate will be the same if b% is given for 1^{st} year and a% is given for 2^{nd} year.
Example: If principal is 1000 Rs and r(1^{st} yr) = 4% and r(2^{nd} yr) = 6%. Calculate the CI after 2yrs.
Solution:
Net CI rate = 4+6+(4×6)/100
= 10.24%
Now CI = 1000×10.24% = 102.4 Rs
Concept6: When difference between CI and SI is given.
We know, net CI for 2yrs = 2r+(r^{2}/100) %,
net SI for 2 yrs = 2r%
So, difference = (r^{2}/100)%
Example: If difference between CI and SI is Rs.10 and the principal is Rs.1000.Calculate the rate % per annum.
Solution: difference = 10 Rs.
So difference% = (10/1000)×100 = 1%
We know that, if rate of interest is 10%
then, net CI rate (2yrs) = 21%
net SI rate (2yrs) = 20%
difference = 1%
Definitely we can say r% per annum is 10%.
Example: Calculate the difference between CI and SI for 3 yrs if Principal = 8000 and r = 6% p.a.
Solution: Net rate CI(3yrs) = 19.1016%
Net rate SI (3yrs) = 18%
Difference = 1.1016%
So, difference = 1.1016% of 8000 = 88.128
Example: If difference between CI and SI is Rs.64 and r = 8% p.a.. Calculate the Principal and Amount?
Solution: If r = 8% p.a.
then, net rate CI (2yrs) – net rate SI (2yrs)
= 16.64% -16% = 0.64%
Given, difference is Rs. 64
So, 0.64% = 64
100% = 10000
Hence, Principal is 10000 Rs.
Amount = principal× (116.64%)= 10000× 116.64% = Rs.11664
Concept7: Calculation of Instalment
Example: A man borrowed Rs.8,400 at 10% p.a. CI. He pays equal annual repayment of X rs and clear off his debts in 2 yrs. What is the value of X?
For 3 yrs: If r% p.a. is given, convert it into fraction(a/b)
Example: A man borrowed Rs.1820 at 20% p.a. CI. He pays equal annual repayment of X rs and clear off his debts in 3 yrs. What is the value of X?
Below is PDF in both Hindi & English:
Compound Interest (English PDF)
चक्रवृद्धि ब्याज पर ट्रिक (हिंदी PDF)
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