Compound Interest Problems For A Bank Exam
Quantitative Aptitude
Study Notes for Bank Exam
You know that quantitative
aptitude section is most important in bank
exams in PO and Clerk and for other competitive exams because if you want
good score in bank exam then you have to score good in maths. In competitive
exams the most important thing is time management, if you know how to manage
your time then you can do well in Bank
Exams as well as in other competitive exams. That’s where maths shortcut tricks and formula are
comes into action. So continuously we are providing shortcut tricks on
different maths topics. Today’s topic is Compound Interest. This is the one of the most important topic in
quantitative aptitude section in bank and SSC exam. You should know how to compound interest problems in very
short time for bank exam. From this
chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks and quicker method to solve compound interest problems in very
short time. Interest is the money paid
by the borrower to the lender for the use of money lent. The sum lent is called
the principal. Interest is usually calculated at the rate of so many rupees for
every Rs 100 of the money lent for a year. This is called the rate per cent per annul.
‘per annum’ means for a year. The
words ‘per annul’ are sometimes omitted. Thus, 6 p.c. means that Rs 6 is the
interest on Rs 100 in one year.
The sum of the principle and
interest is called the amount.
The interest is usually paid
yearly, half-yearly or quarterly as agreed upon.
COMPOUND
INTEREST: Money is
said to be lent oat compound Interest (CI) when at the end of a year or other
fixed period the interest that has become due is not paid to the lender, but is
added to the sum lent, and the amount thus obtained becomes the principal for
the next period. The process is repeated until the amount for the last period
has been found. The difference between the original principal and the final
amount is called Compound Interest (CI).
IMPORTANT
FORMULAE FOR COMPOUND INTEREST:
Let Principal = P
Time = t yrs
Rate = r% per annul
Case 1. When interest is compounded annually:
Amount = P(1+r/100)^n
Case 2. When interest is compounded half yearly,
Amount = P(1+(r/2)/100)^2n
Case 3. When interest is compounded Quarterly,
Amount =P(1+(r/4)/100)^4n
Case 4. When interest is compounded annually but time is
in fraction, say 3 whole 2/5 year
Amount =
P(1+r/100)^3×(1+(2r/5)/100)
Case 5. When Rates are different for different years, say
r1%, r2%, and r3% for 1st, 2nd and 3rd year respectively.
Then,
Amount = P(1+r1/100)×(1+r2/100)×(1+r3/100).
Present worth of Rs. x due n
years hence is given by:
Present Worth = x/(1+r/100)
Difference
between Compound Interest & Simple interest Concept For Two
years
CI – SI =P(r/100)^2
For Three Year
CI – SI =P(r^2/(100^2
))×(300+r)/100)
For Two year
CI/SI=(200+r)/200
The above mentioned formulae are
not new for you. We think that all of you know their uses. When dealing with
the above formulae, some mathematical calculations become lengthy and take more
time. To simplify the calculations and save the valuable time we are giving
some extra information. Study the following sections carefully and apply them
during your calculations.
The problem are generally asked
upto the period of 3 years and the rates of interest are 10%, 5% and 4%.
We have the basic formula:
Amount = Principal(rate/100)^time
If the principal is Rs 1, the
amount for first, second and third years will be
(1+r/100), (1+r/100)2
and (1+r/100)3.
And, if the rate of interest is
10%, 5% and 4%, these value will be:
TIME
|
1 YEAR
|
2 YEARS
|
3 YEARS
|
r
|
(1+r/100),
|
(1+r/100)2
|
(1+r/100)3
|
10
|
11/10
|
121/100
|
1331/1000
|
5
|
21/20
|
441/400
|
9261/8000
|
4
|
26/25
|
676/625
|
17576/15625
|
The above table should be
remembered. The use of the above table can be seen in the following examples.
COMPOUND
INTEREST QUESTIONS WITH ANSWERS:
Ex. 1: Rs. 7500 is borrowed at CI at the rate of 4% per
annum. What will be the amount to be paid after 2 years?
Solution: as the rate of interest
is 4% per annum and the time is 2 yrs. Our concerned fraction would be 676/625.
Form the above table, you know taht Rs 1 becomes Rs 676/625 at 4% per annum
after 2 yrs. So, after 2 yrs Rs 7500 will produce 7500 * 676/625
= rs 8112.
Ex.
2: What will be the compound interest on a sum of Rs. 25,000 after 3 years at
the rate of 12 p.c.p.a.?
Solution:
Amount = Rs. 25000(1+12/100)^3= 35123.20
So
CI= Rs. (35123.20 - 25000) = Rs. 10123.20
To
find the % difference between CI and SI
Ex.
3: to find the % difference between CI and SI, for 2 yrs if rate of interest is
4%.
Solution:
SI
= 2 * 4 = 8% of capital
CI
= 4 + 4 + 4*4/100
=2*4
+ 16/100
=
8.16% per capital
Ex. 4: The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
Solution:
SI =Rs. (1200 ×10×1)/100= Rs. 120
CI
= Rs. [ 1200×(1+5/100) ^2 - 1200] = Rs.123
So
CI-SI = Rs. 3
To
find time:
Ex.
5: in what time will Rs 390625 amount to Rs 456976 at 4% compound interest?
Solution:
P(1+r/100)t
= A
390625(1+4/100)t
= 456976
(1+1/25)t
= 456956 / 390625
(26/25)t
= (26/25)4
T
= 4
The
required time is 4 years
Ex.
6: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period
(in years) is:
Solution:
Amount
= Rs. (30000 + 4347) = Rs. 34347,
Let
the time be n years then
30000(1+7/100)
^n = 34347
(107/100)
^n = 34347/30000
So
n = 2 year.
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