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.3100
(b) Rs.2980
(c) Rs.3109
(d) Rs.3091
The correct answers to the above question in:
Answer: (c)
Using Rule 1,
Amount = P$(1 + R/100)^t$
= 8000$(1 + 15/100)^{2{1}/3}$
= 8000$(1 + 3/20)^2(1 + 3/{20 × 3})$
= $8000 × 23/20 × 23/20 × 21/20$ = Rs.11109
Compound Interest
= Rs.(11109 - 8000) = Rs.3109.
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Read more basic problems using formula Based Quantitative Aptitude Questions and Answers
Question : 1
The compound interest on Rs.6,000 at 10% per annum for 1$1/2$ years, when the interest being compounded annually, is
a) Rs.900
b) Rs.910
c) Rs.930
d) Rs.870
Answer »Answer: (c)
Amount = 6000$(1 + 10/100) × (1 + {{1/2} × 10}/100)$
= $6000 × 11/10 × 21/20$ = Rs.6930
Using Rule 4,If the time is in fractional form i.e.,t = nF, thenA = P$(1 + r/100)^n(1 + {rF}/100)$e.g. t =3$5/7$ yrs, thenA = P$(1 + r/100)^3(1 + r/100 × 5/7)$
Here, t = nF
A = P$(1 + r/100)^n(1 + {rF}/100)$
CI = Rs.(6930 - 6000) = Rs.930
Question : 2
A sum becomes Rs.1,352 in 2 years at 4% per annum compound interest. The sum is
a) Rs.1,250
b) Rs.1,225
c) Rs.1,245
d) Rs.1,270
Answer »Answer: (a)
Using Rule 1,
Let the sum be Rs.x.
1352 = $x(1 + 4/100)^2$
1352 = $x(1 + 1/25)^2$
$1352 = x(26/25)^2$
$x = {1352 × 25 × 25}/{26 × 26}$ = Rs.1250
Question : 3
At what rate per annum will Rs.32000 yield a compound interest of Rs.5044 in 9 months interest being compounded quarterly ?
a) 80%
b) 20%
c) 50%
d) 32%
Answer »Answer: (b)
Using Rule 1,
Let the rate of CI be R per cent per annum.
CI = P$[(1 + R/100)^T - 1]$
5044 = 32000$[(1 + R/400)^3 - 1]$
[Since, Interest is compounded quarterly]
$5044/32000 = (1 + R/400)^3 - 1$
$(1 + R/400)^3 - 1 = 1261/8000$
$(1 + R/400)^3 = 1 + 1261/8000$
$(1 + R/400)^3 = 9261/8000 = (21/20)^3$
1 + $R/400 = 21/20$
$R/400 = 21/20 - 1 = 1/20$
R = $400/20$ = 20
Question : 4
A certain sum amounts to Rs.5,832 in 2 years at 8% per annum compound interest, the sum is
a) Rs.5,400
b) Rs.5,000
c) Rs.5,280
d) Rs.5,200
Answer »Answer: (b)
Using Rule 1,
5832 = P$(1 + 8/100)^2$
5832 = P$(1 + 2/25)^2$
5832 = P $× 27/25 × 27/25$
P = ${5832 × 25 × 25}/{27 × 27}$ = Rs.5000
Question : 5
The compound interest on Rs.30,000 at 7% per annum for a certain time is Rs.4,347. The time is
a) 2.5 years
b) 3 years
c) 2 years
d) 4 years
Answer »Answer: (c)
Using Rule 1,
A = P$(1 + R/100)^T$
30000 + 4347 = $30000(1 + 7/100)^T$
$34347/30000 = (107/100)^T$
$11449/10000 = (107/100)^2 = (107/100)^T$
Time = 2 years
Question : 6
In what time will Rs.1000 amounts to Rs.1331 at 20% per annum, compounded half yearly ?
a) 2$1/2$ years
b) 1$1/2$ years
c) 1 year
d) 2 years
Answer »Answer: (b)
Using Rule 1 and 2,
Let the required time be t years. Interest is compounded half yearly.
Time = 2t half years and rate
= $20/2$ = 10%
1000$(1 + 10/100)^{2t}$ = 1331
$(11/10)^{2t} = 1331/1000$
$(11/10)^{2t} = (11/10)^3$ ⇒ 2t = 3
t = $3/2$ years or 1$1/2$ years
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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