SSC CGL 24 Aug 2021 Shift 3 Paper

Question : 75 of 100

Marks: +1, -0

What is the difference between the compound interest (in ₹) compounded yearly and compounded half-yearly for 18 months at

20 \%

p.a. on a sum of ₹ 12000 ?

Solution:

For compound interest yearly.

P=₹ 12000, R=20 \%

T=18

months

=1+\;{6}/{12}=1 \;{1}/{2} {yr}

∴ {Cl}=P[(1+\;{R}/{100})^{T}(1+\;{R × {a}/{b}}/{100})-1]

=12000[(1+\;{20}/{100})^{1}(1+\;{20 × {1}/{2}}/{100})-1]

=12000[\;{6}/{5} × \;{11}/{10}-1]=12000[\;{33-25}/{25}]

=480 × 8=₹ 3840

for compound interest half yearly

P=₹ 12000, R=\;{20}/{2}=10 \%, T=3

∴ {Cl} \;\; =P[(1+\;{R}/{100})^{T}-1]

\;\; =12000[(1+\;{10}/{100})^{3}-1]

\;\; =12000[\;{1331}/{1000}-1]

\;\; =12000[\;{1331-1000}/{1000}]

\;\; =12 × 331=₹ 3972

∴ \;\text " Required difference "\;

\;\; =3972-3840=132

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