model 4 difference in ci & si Practice Questions Answers Test with Solutions & More Shortcuts
compound interest PRACTICE TEST [6 - EXERCISES]
model 1 basic compound interest using formula
model 2 at ci sum becomes ‘n’ times after ‘t’ years
model 3 combination of si & ci
model 4 difference in ci & si
model 5 ci with instalments
model 6 comparing sum in different years
Question : 11 [SSC CGL Prelim 2000]
What is the difference between compound interest on 5,000 for 1 1 2 years at 4% per annum according as the interest is compounded yearly or halfyearly?
a) 4.80
b) 2.04
c) 8.30
d) 3.06
Answer »Answer: (d)
Compound Interest (when compounded yearly)
= $5000(1 + 4/100)^(1.5) - 5000$
= $5000(26/25)^(1.5) - 5000$
= 5302.9805 - 5000 = Rs.302.9805
C.I. (When compounded halfyearly).
= $5000(1 + 2/100)^3 - 50000$
= 5306.04 - 5000 = Rs.306.04
Required difference
= Rs.(306.04 - 302.9805)
= Rs.3.059 = Rs.3.06
Question : 12 [SSC CGL Prelim 2004]
The difference between the compound interest (compounded annually) and the simple interest on a sum of 1000 at a certain rate of interest for 2 years is 10. The rate of interest per annum is :
a) 12%
b) 5%
c) 10%
d) 6%
Answer »Answer: (c)
When difference between the compound interest and simple interest on a certain sum of money for 2 years at r% rate is x, then
x = Sum$(r/100)^2$
10 = 1000$(r/100)^2$
$(r/100)^2 = 10/1000$
$r/100 = √{1/100} = 1/10$
r = $100/10$ = 10%
Using Rule 6,
Here, C.I. - S.I. = Rs.10, R = ?, T= 2 years, P = Rs.1000
C.I. - S.I. = P$(R/100)^2$
10 = 1000$(R/100)^2$
10 = 1000$ × R/100 × R/100$
$R^2$ = 100
R = $√{100}$ = 10%
Question : 13 [SSC CPO S.I.2007]
The difference between compound interest (compounded annually) and simple interest on a certain sum of money at 10% per annum for 2 years is 40. The sum is :
a) 3200
b) 4000
c) 4200
d) 3600
Answer »Answer: (b)
Let the principal be x.
Compound interest
= P$[(1 + R/100)^t - 1]$
= $x[(1 + 10/100)^2 - 1]$
= $x[(1.1)^2 - 1]$
= x (1.21 - 1) = 0.21x
SI = ${x × 2 × 10}/100 = x/5 = 0.2x$
According to the question,
0.21x - 0.2x = 40
$0.01x = 40 ⇒ x = 40/{0.01}$ = Rs.4000
Using Rule 6,
Here, C.I. - S.I. = Rs.40, R = 10%, T = 2 years, P = ?
C.I. - S.I. = P$(R/100)^2$
40 = P$(10/100)^2$ ⇒ P = Rs.4000
Question : 14 [SSC CGL Tier-1 2011]
The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is 48. Then the sum is
a) 2, 000
b) 1,000
c) 1, 500
d) 1, 200
Answer »Answer: (d)
Using Rule 6,
Difference of two years
= P$(r^2/10000)$
48 = P$(400/10000)$
48 = $P/25$
P = 48 × 25 = Rs.1200
Question : 15 [SSC MTS 2013]
The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is 1.50. The sum is
a) 300
b) 600
c) 400
d) 500
Answer »Answer: (b)
Using Rule 6,
Difference = ${PR}^2/(100)^2$
1.50 = ${P × 5 × 5}/(100)^2$
P = 400 × 1.5 = Rs.600
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model 4 difference in ci & si Shortcuts »
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Click to Start..compound interest Shortcuts and Techniques with Examples
-
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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