COMPOUND INTEREST
Compound Interest: The interest is calculated on the principal as well as on the interest, that’s why the interest is not constant. The interest as well as principal varies from time to time. Principal with interest is second year principal, similarly second year principal with interest is third year principal and so on.
Generally, the problems on S.I & C.I are based on the calculation of percentage i.e. on the out of 100. So if we calculate the S.I & C.I. on a sum of 100 @ any % it is easy to get. Then we can calculate the S.I. & C.I. on the given sum
COMPOUND INTEREST:
CONCEPT: The general concept regarding C.I is as follows:
If the sum is Rs100 and the rate of interest is R% p.a. then the ratio between the sum and the amount is as follows:
After T years the ratio between sum and the amount is 100n: (100+R)n
So if we get the amount then the C.I is Amount- Principal.
Then we can find out the C.I on different sum at different rate of interest easily.
And also we can find out the time period as well as the rate of interest on the given data easily.
DIFFERENT TPPES OF PROBLEMS BASED ON C.I.
QUESTION: Find the C.I on a sum of Rs16000 @ 5% p.a. for 3 years.
Sol: If the sum is Rs100, then @ 5% p.a. the amount is Rs105.
So the ratio between the principal & amount is 20:21 after 1 year.
There fore the ratio between the principal & amount after 3 years is 203:213
So when the principal is 8000, the amount is 9261 in which the C.I is Rs1261.
If the principal is Rs16000, then the C.I is Rs2522.
QUESTION:
Find the C.I on a sum of Rs24000 @20% p.a. for 1 year if the sum is compounded half yearly.
Sol: If the rate of interest is 20% p.a. then half yearly it is 10%.
So if the sum is Rs100, then after 6 months the amount is 110 in which the ratio between the sum & principal is 10:11.
In 1 year the sum compounded 2 times at which the ratio between the sum & amount is 102:112.
When the sum is 100 the amount is 121, so that the C.I is Rs21.
So when the sum is Rs24000, the C.I is Rs5040.
QUESTION:
Find the C.I on Rs16000 @ 20% p.a. for 9 months, if the principal compounded quarterly.
Sol: If the rate of interest is 20% p.a. quarterly it is 5%. So 100 becomes 105 after 3 months in which the ratio is 20:21 and in 9 months the sum is compounded 3 times in which the ratio is 203: 213.
When the sum is Rs8000 the amount is Rs9261 in which the C.I is Rs1261.
So if the sum is Rs16000, the C.I is Rs2522.
QUESTION:
If Rs16000 amounts to Rs18522 in 3 years, find the rate of interest p.a.
Sol: The ratio between the sum & amount after 3 years is 8000: 9261.
So after the ratio between the sum & amount is the cube root of 8000: 9261 i.e. 20-:21
When the sum is 20 parts the interest is 1 part.
So when the sum is 100, the interest is 5 i.e. 5% p.a.
QUESTION:
If Rs24000 amounts to Rs27783 at the rate of 5% p.a. at C.I, find the time period.
Sol: If the sum is 100, then the amount is 105 after 1 year in which the ratio is 20:21.
In this case the ratio between sum & amount is 8000:9261 which is cube of the above ratio of 20:21.
So the time period is 3 years.
QUESTION:
Rs125000 is borrowed at C.I @2% for the first year, 3% for the second year and 4% for the third year. Find the amount to be paid after 3 years.
Sol: If the sum is Rs100, then after 1 year the amount is 102, then after second year the amount is 105.06 and after 3 years the amount is 109.2624.
When sum is 100, the amount is 109.2624.
So when the sum is Rs125000, the amount is Rs136578.
QUESTION:
A sum of money placed at C.I doubles itself in 8 years. In how many years will it amount to 8 times itself?
Sol: If sum is 1 part, then the amount is 2 parts in 8 years.
So when the amount is 8 parts i.e. 23 parts in 24 years
QUESTION:
At what rate percent C.I does a sum of money become 9 fold in 2 years?
Sol: If sum is 100, the amount is 900 in which the ratio is 1:9.after 2 years.
So, after 1 year the ratio is the square root of 1:9 i.e. 1:3.
In this case the interest is 2 parts on a sum of 1 part which is @ 200% p.a.
QUESTION:
The S.I on a certain sum of money for 2 years @ 10% p.a. is Rs4800. Find the C.I on the same sum at the same rate for the same period.
Sol: The S.I is constant for each & every year. So the interest is Rs2400 each year.
But in case of C.I the interest in the first year is Rs2400, in the second year the interest is 10% more than the second year i.e. Rs2640.
So the C.I is Rs2400+Rs2640= Rs5040.
QUESTION:
The S.I on a certain sum of money for 3 years @ 10% p.a. is Rs3600. Find the C.I on the same sum at the same rate for the same period.
Sol: The S.I in each & every year is Rs1200.
So the C.I in the first year is Rs1200, in the second year is 10% more than first year i.e. Rs1320 & in the third year is Rs1452.
Therefore the C.I is Rs1200+1320+1452= Rs3972.
QUESTION:
The C.I on a certain sum of money for 2yrs @ 5% p.a. is Rs8200. Find t S.I on the same sum at the same rate for the same period.
Sol: If the sum is Rs100 then the C.I in 2 years is as follows.
In the first year it is Rs5, in the second year it is Rs5.25. So in 2 years the C.I is Rs10.25.
But at the same time the S.I is Rs10 in 2 years on Rs100.
When C.I is Rs10.25, The S.I is Rs10.
So when C.I is Rs8200, the S.I is Rs8000
QUESTION:
The C.I on a certain sum of money @ 10% p.a. for 3 years is Rs6620. Find the S.I on the same sum at the same rate for the same period.
Sol: If the sum is Rs100, the C.I in the first year is Rs10, in the second year it is Rs11 & in the third year it is Rs12.10.
So when the C.I is Rs33.10, the S.I is Rs30.
When C.I is Rs6620, the S.I is Rs6000.
QUESTION:
The C.I on a certain sum of money for 2 years is Rs40.80 and the S.I is Rs40. Find the rate of interest & the sum.
Sol: The S.I is Rs40 means that in each year it is Rs20. So that the C.I in the first year is Rs20 & in the second year it is Rs20.80
This Rs0.80 is the interest on the interest of Rs20 which is @4% p.a.
To find out the sum, if the sum is Rs100 in 2 years @4% p.a. it is Rs8.
So when the interest is Rs8, the sum is Rs100.
When the interest is Rs40, the sum is Rs500.
QUESTION:
On a certain sum of money, the S.I for 2 years is Rs160@5% p.a. Find the difference in C.I & S.I.
Sol: If the S.I is in 2 years is Rs160, in each year it is Rs80.
So the difference in C.I & S.I in 2 years is 5% on the interest of Rs80 i.e. Rs4.
QUESTION:
The difference between the C.I & S.I on a certain sum of money at 8% p.a. for 2 years is Rs40. Find the sum.
Sol: If the sum is Rs100, the C.I is Rs16.64 & S.I is Rs16, So the difference is Rs0.64.
When the difference is Rs0.64, the sum is Rs100.
So when the difference is Rs40, the sum is Rs6250.
QUESTION:
If the difference between the C.I & S.I for 3 years @ 10% p.a. is Rs620, find the sum.
Sol: If the sum is Rs100, then the C.I in 3 years is Rs33.10 & S.I is Rs30 in which the difference is Rs3.10.
When the difference is Rs3.10, the sum is Rs100.
So when the difference is Rs620, the sum is Rs20000.
QUESTION:
Find the ratio of C.I & S.I on a sum at 8% p.a. for 2 years.
Sol: If we take the sum as Rs100, then the C.I is Rs16.64 & S.I is Rs16.
So the ratio is 26:25
QUESTION: An amount at C.I is Rs6560 in 3 years & Rs7216 in 4 years. Find the rate percent per annum.
Sol: The interest in 1 year is Rs656 on a sum of Rs6560 which is @ 10% p.a.
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