model 1 basic compound interest using formula Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on compound interest topic of quantitative aptitude
(a) Rs.828. 82
(b) Rs.636.80
(c) Rs.912. 86
(d) Rs.824.32
The correct answers to the above question in:
Answer: (d)
Using Rule 1,
A = 10,000$(1 + 2/100)^4$
=10,000$(51/50)^4$ =10824.3216
Interest = 10,824.3216 - 10,000
= Rs.824.32
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Read more basic problems using formula Based Quantitative Aptitude Questions and Answers
Question : 1
A man borrows Rs.21000 at 10% compound interest. How much he has to pay annually at the end of each year, to settle his loan in two years ?
a) Rs.12300
b) Rs.12000
c) Rs.12200
d) Rs.12100
Answer »Answer: (d)
If each instalment be x, then Present worth of first instalment
= $x/{1 + 10/100} = {10x}/11$
= Present worth of second instalment
= $x/(1 + 10/100)^2 = 100/121x$
$10/11x + 100/121x$ = 21000
${110x + 100x}/121 = 21000$
210x = 21000 × 121
$x = {21000 × 121}/210$ = Rs.12100
Using Rule 9,If a sum 'P' is borrowed at r% annual compound interest which is to be paid in 'n' equal annual installments including interest, then(i) For n = 2, Each annual installment= $p/{(100/{100 + r}) + (100/{100 + r})^2$(ii) For n = 3, Each annual installment= $p/{(100/{100 + r}) + (100/{100 + r})^2 + (100/{100 + r})^3$
Here, n = 2, p = Rs.21000, r = 10%
Each annual instalment
= $p/{(100/{100 + r}) + (100/{100 + r})^2$
= $21000/{100/110 + (100/110)^2}$
= $21000/{100/110 + 10000/12100}$
= $21000/{10/11 + 100/121}$
= $21000/{110 + 100} × 121$
= $21000/210 × 121$ = 12100
Question : 2
A certain sum, invested at 4% per annum compound interest, compounded half yearly, amounts to Rs.7,803 at the end of one year. The sum is
a) Rs.7,700
b) Rs.7,000
c) Rs.7,500
d) Rs.7,200
Answer »Answer: (c)
Using Rule 1,
Let the sum be P.
As, the interest is compounded half-yearly,
R = 2%, T = 2 half years
A = P$(1 + R/100)^T$
7803 = P$(1 + 2/100)2$
7803 = $(1 + 1/50)^2$
7803 = P$× 51/50 × 51/50$
P = ${7803 × 50 × 50}/{51 × 51}$ = Rs.7500
Question : 3
In how many years will Rs.2,000 amounts to Rs.2,420 at 10% per annum compound interest?
a) 1$1/2$ years
b) 3 years
c) 2 years
d) 2$1/2$ years
Answer »Answer: (c)
Using Rule 1,
According to question,
2420 = 2000$(1 + 10/100)^t$
$2420/2000 = (11/10)^t$
or $(11/10)^t = 121/100$
or, $(11/10)^t = (11/10)^2$
t = 2 years
Question : 4
The compound interest on Rs.2000 in 2 years if the rate of interest is 4% per annum for the first year and 3% per annum for the second year, will be
a) Rs.143.40
b) Rs.142.40
c) Rs.141.40
d) Rs.140.40
Answer »Answer: (b)
Using Rule 3,
Amount = $2000(1 + 4/100)(1 + 3/100)$
= 2000 ×1.04 ×1.03 = Rs.2142.40
CI = Rs.(2142.40 - 2000) = Rs.142.40
Question : 5
An amount of Rs.6,000 lent at 5% per annum compound interest for 2 years will become
a) Rs.6,615
b) Rs.600
c) Rs.6,610
d) Rs.6,600
Answer »Answer: (a)
Using Rule 1,
A = P$(1 + R/100)^T$
= 6000$(1 + 5/100)^2$
= 6000 × $21/20 × 21/20$ = Rs.6615
Question : 6
The sum of money that yields a compound interest of Rs.420 during the second year at 5% p.a is
a) Rs.21,000
b) Rs.4,000
c) Rs.8,000
d) Rs.42,000
Answer »Answer: (c)
Using Rule 1,
CI = P$[(1 + R/100)^T –1] - {PR}/100$
420 = P$[(1 + 5/100)^2 - 1] - {P × 5}/100$
420 = P$[(21/20)^2 - 1] - {5P}/100$
420 = ${41P}/400 - {5P}/100 = {21P}/400$
P = ${420 × 400}/21$ = Rs.8000
compound interest Shortcuts and Techniques with Examples
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model 1 basic compound interest using formula
Defination & Shortcuts … -
model 2 at ci sum becomes ‘n’ times after ‘t’ years
Defination & Shortcuts … -
model 3 combination of si & ci
Defination & Shortcuts … -
model 4 difference in ci & si
Defination & Shortcuts … -
model 5 ci with instalments
Defination & Shortcuts … -
model 6 comparing sum in different years
Defination & Shortcuts …
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