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COMPOUND INTEREST
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Page 1 of 18
Preface The Digi-notes (Compound Interest) as presented here is prepared strictly according to IBPS-PO, IBPS-Clerk, IBPS-SO and other PO/Clerk level competitive exams. The main aim of the Digi-notes is to develop the notion of the Compound Interest so that candidate would be able to handle the quantitative problems easily and conveniently in their competitive exams. Candidates are advised to handle the Digi-notes by keeping in mind that they are going to LEARN (NOT STUDY) the Compound Interest so that you; yourself would be able to minimize the steps required to conclude the answer of the question and hence develop the SHORT TRICKS.
Introduction: Likewise as in simple interest; in compound interest also we will use the formulae rarely. The compound interest formulae are too costly to use in terms of time and calculation. We will learn in the coming section that how to use; again; the percentage tool to solve the compound interest questions in nearly 90% of the questions.
Approach for Compound Interest Questions:
In IBPS PO, IBPS Clerk, IBPS SO and other competitive examinations; if the examiner asks directly the question to find the compound interest or simple interest or their difference; they are mainly focussing on 2 years’ time and 3 years’ time. In rare case; only 2 to 3 times; the Page 4 of 18
question related to 4 years’ time is asked; and that’s too easy. So our main focus will be on 2 years’ question and 3 years’ question. Next we are going to discuss the SLAB METHOD approach for cracking the verities of questions related to compound interest. If P is the principle and r% is the the rate of interest:
1. For 2 year: Short Trick: I
P
II P
r 100
r
P
100
r
r
100
100
Learn the following properties:
2. For 3 year: I
r
P
100
II P III P
r 100
r 100
P P
r
r
r
100 100
r
100 100
P
r
r
100 100
P
r
r
r
100 100 100
Page 5 of 18
Learn the following properties:
Page 6 of 18
Questions: Now we are equipped enough to solve the following questions: Q.1: Find the compound interest on Rs.58800 at years; compounded annually.
%
Sol: I
Rs.8400
II
Rs.8400
≡
% pa
after 2
% pa
after 3
Rs.1200
CI 2 Rs.8400 Rs.1200 Rs.18000
Q.2: Find the compound interest on Rs.32400 at years; compounded annually.
Q.3: Find the difference between the compound interest and the simple interest at 5% pa on Rs.1842 after 2 years; compounded annually. Page 7 of 18
Sol:
I
Rs.92.10
II
Rs.92.10
Rs.4.605
CI SI Rs.4.605
Q.4: Find the difference between the compound interest and the simple interest at % pa on Rs.1280 after 3 years; compounded annually. Sol:
12 % ≡ 8
I
Rs.160
II
Rs.160
Rs.20
III
Rs.160
Rs. 20
Rs.20
Rs. 2.5
CI SI 3 Rs.20 Rs. 2.5 Rs .62.50
Q.5: The simple interest on a certain sum of money at 3% pa after 2 years is Rs.80. Find the compound interest on the same sum of money at the same rate after 2 years.
Sol:
I
Rs.40
II
Rs.40
Rs.1.2
CI Rs.81.20
Page 8 of 18
Q.6: The simple interest on a certain sum of money at 5% pa after 3 years is Rs.150. Find the difference between the compound interest and the simple interest on the same sum of money at the same rate after 3 years. Sol: I
Rs.50
II
Rs.50
Rs.2.5
III
Rs.50
Rs.2.5
Rs.2.5
Rs. 0.125
CI SI 3 Rs. 2.5 Rs. 0.125 Rs .7.625
Q.7: The simple interest on a certain sum of money at a certain rate of interest after 2 years is Rs.84 and the compound interest on the same sum of money at the same rate after 2 years is Rs.86.10. Find the rate of the interest per annum and the principle. Sol:
Now
I
Rs.42
II
Rs.42 42
42
r
100
r
5%
And P 42 42
Rs.2.1 Rs.2.1
p.a.
100
5
Rs.840
Q.8: The difference between the compound interest and the simple interest on a certain sum of money at 5% pa after 2 years is Rs.1.50. Find: 1. The Principle Page 9 of 18
2. The Simple Interest 3. The compound Interest Sol: P Rs.600 I
Rs.30
II
Rs.30
Rs.1.50 .1.50
SI Rs .60 CI Rs .61.50
Q.9: The compound interest on a certain sum of money at 20% pa after 2 years is Rs.243.10. Find the simple interest on the same sum of money at the same rate after 2 years. y ears. Sol:
Let P ≡ 25% ← Square (≡ 2 years) of Denomin Denominato atorr of 20% 20% ≡ P
SI
25%
I
5%
II
5% 5%
Rs.243.10 11%
1%
10%
Rs.221
Q.10: The compound interest on a certain sum of money at pa after 2 years is Rs.585.26. Find
%
1. Principle Page 10 of 10 of 18
2. The simple interest on the same sum of money at the same rate after 2 years. Let P ≡ 36% ← Squ Square (≡ Sol:Let 2 years) of Denominator of 16 % ≡
P
P
1
2
SI
36%
I
6%
II
6% 6%
Rs.585.26
1%
36%
13%
Rs.585.26
Rs.1620.72
12%
13%
Rs.540.24
Q.11: The difference between the compound interest and the simple interest on a certain sum of money at % pa after 3 years is Rs.350. Find the difference between the compound interest and the simple interest on the same sum of money at the same rate after 2 years? Sol: Let P ≡ 729% ← Cube (≡ (≡ 3 years) of Denominator of 11 % ≡ P 729%
I
81%
II
81%
9%
III
81%
9%
CI SI 2 years
Rs.350 28%
9%
1%
9% Rs.112.50
Page 11 of 11 of 18
Q.12: The compound interest of the third year on a certain sum of money at % pa is Rs.7680. Find the compound interest on the same sum of money at the same rate after 2 years. Let P ≡ 343% ← Cube (≡ Sol:Let 3 years) of Denominator of 14 % ≡ P 343%
I
49%
II
49%
7%
III
49%
7%
CI After 2 years
Rs.7680 64%
7%
1%
105% Rs.12600
Q.13: The difference between the compound interest of the third year and the compound interest of the second year on a certain sum of money at % pa is Rs.98. Find the sum. Sol:Let P ≡ 216% ← Cube (≡ (≡ 3 years) of Denominator of 16 % ≡ P 216%
I
36%
II
36%
6%
III
36%
6%
P
Rs.98 7%
6%
1%
216% Rs.3024
Page 12 of 12 of 18
Q.14: The respective ratio of the difference between the compound interest and the simple interest on a certain sum of money after 3 years and the difference between the compound interest and the simple interest on the same sum after 2 years is 25:8. Find the rate of the interest. Sol: I II
8
III
8
8
r 100
8
1
1 1
r 12 % pa 2
Q.15: Find the compound interest on Rs.8000 after 2 years; the rate of the interest being 4% pa for the first years and 6% pa for the second year. Rs.8000 4% I
Rs.320
6% II
Rs.480
Rs.19.20
CI Rs R s.320 Rs .480 Rs .19.20 Rs .819.20
Page 13 of 13 of 18
Q.16: Find the compound interest on Rs.10000 after 3 years; the rate of the interest being 4% pa for the first years; 5% pa for the second years and 6% pa for the third year. Short Trick: Rs.10000
Q.17: Find the compound interest on Rs.5000 at 20% pa after years; the interest being compounded annually.
Short Trick: Rs.5000 20% Y
Rs.1000
10% HY
Rs.500
Rs.100
CI Rs.1600
Q.18: Find the compound interest on Rs.5000 at 20% after years; the interest being compounded half yearly.
Short Trick: Rs.5000
10 10% HY1
Rs.500
10% HY2
Rs.500
Rs.50
10% HY3
Rs.500
Rs.50
Rs.50
Rs R s. 5
CI Rs.1650
Page 14 of 14 of 18
Q.19: Find the compound interest on Rs.5000 at 20% after years; the interest being compounded half yearly.
Short Trick: Rs.5000 10 10% HY1
Rs.500
10% HY2
Rs.500
Rs.50
HY Rs.250 2 CI Rs.1352.50
Rs.25
5%
1
Rs R s.25
Rs Rs.2.5
Q.20: Find the difference between the compound interest on Rs.2000 at 10% pa after years; when compounded annually and compounded half yearly?
Rs.2000
Rs.2000
Sol:
10% Y
Rs.200
5% HY
Rs.100
Rs.10
CI Rs.310
5% 5% HY1
Rs.100
5% HY2
Rs.100
Rs.5
5% HY3
Rs.100
Rs.5
Rs.5
Rs.0.25
CI Rs.315.25
Requ Requir ired ed Diff Differ eren ence ce = 315. 315.25 25 − 310 310 = Rs. Rs. 5.25 5.25
Q.21: Find the compound interest on Rs.2000 at 20% pa after 9 months; the interest being compounded quarterly? Rs.2000
5% 5% Q1
Rs.100
5% Q2
Rs.100
Rs.5
5% Q3
Rs.100
Rs.5
Rs.5
Rs.0.25
CI Rs.315.25 Page 15 of 15 of 18
Q.22: A certain sum of money grows to 40759 after 2 years at a certain rate of interest; compounded annually; while grows to Rs.44834.90 after 2 years at the same rate; compounded annually. Find the rate of interest and principle. Short Trick: 40759
Sol:
r 100
40759
44834.90 40759 r
100
4075.90
r 10%
Q.23: A certain sum of money grows to 7290 after 6 years at a certain rate of interest; compounded annually; while grows to Rs.531441 after 12 years at the same rate; compounded annually. Find the rate of interest and principle. Short Trick: Sol: P
A62 years A12 years
Rs.182250 Rs.531441
2
Rs.
Q.24: A certain sum of money grows to 3 times of itself at a certain rate of interest; compounded half yearly; after 2 years. In how many years would the same sum of money grows to 27 times of itself. Short Trick: Sol:
2 3 ⏟ 2 ⏟ ⏟
9 ⏟ 2 27 6
Page 16 of 16 of 18
Q.25: After how many years; compounded yearly; would Rs.1875 grows to Rs.2028 at 4% pa? Short Trick: CI Rs.2028 Rs.1875 Rs.153 P=1875
Sol:
Y 2 years Y
Rs.75 Rs.75
Rs.3
Hence after 2 years.
Q.26: After how many years; compounded half yearly; would Rs.800 grows to Rs.926.10 at 10% pa? Short Trick: Sol: P Rs.800
1 Rs.40 2 Y 1 3 half ye years Y Rs.40 2 1 2 Y Rs.40 CI 126.10 926.10 800 Hence aftre r 1
1 2
Rs.2 Rs.2
Rs.2
Rs .0.1
years
Q.27: At what rate percent per annum; compounded annually; will Rs.80000 amount to Rs.88200 in 2 years?
