SSC CGL 17 Aug 2017 Shift 1 Paper

Question : 60 of 100

Marks: +1, -0

What is the difference (in ₹) between the compound interests on₹ 4000 for 1 year at 12% per annum compounded yearly and half-yearly?

Solution:

For 1 year, C.I. and S.I. are same.
Therefore,
C.I.

= {\S.\I.}= {P × R× T}/{100}

= {4000×12 ×1}/{100}=\₹ 480

If the C.I. compounded halfyearly, then

r= {12}/{2}=6 \%

and time

(n)=1 × 2=2

New, C.I.

=P [ (1+ {r}/{100} )^{n}-1 ]

=4000[(1+ {6}/{100} )^{2}-1 ]

=4000[( 106 /{100} )^{2}-1 ]

=4000[{106^{2}-100^{2}}/{100^{2}} ]

= {4000(106+100)(106-100)}/{100 × 100}

= {4000×206 × 6} / {100×100} =\₹494.4

∴ Required difference

=494.4-480=\₹ 14.4

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