Question

calculate the amount and the compound interest on rupees 32000 for 6 months at 5% per annum compounded quarterly​

Answer 1

AnswEr :

$\bf{\red{\underline{\underline{\mathcal{GIVEN\::}}}}}$

• Principal,[P] = Rs.32000
• Rate,[R] = 5% per annum
• Time,[n] = 6 months.

$\bf{\red{\underline{\underline{\mathcal{TO\:FIND\::}}}}}$

• The amount.
• The compound Interest.

$\bf{\red{\underline{\underline{\mathcal{EXPLANATION\::}}}}}$

Formula use : (For compounded quarterly).

$\bf{\boxed{\sf{A=P\bigg(1+\frac{R}{4\times 100} \bigg)^{4n} }}}}$

A/q

$\leadsto\sf{Time\:=\:6\:months=\cancel{\dfrac{6}{12} }}=\red{\dfrac{1}{2} \:years}}}$

Now;

$\mapsto\sf{A=32000\bigg(1+\dfrac{5}{4\times 100} \bigg)x^{\cancel{4}\times \dfrac{1}{\cancel{2}} }} \\\\\\\mapsto\sf{A=32000\bigg(1+\cancel{\dfrac{5}{400}} \bigg)^{2} }\\\\\\\mapsto\sf{A=32000\bigg(1+\dfrac{1}{80} \bigg)^{2} }\\\\\\\mapsto\sf{A=32000\bigg(\dfrac{80+1}{80} \bigg)^{2} }\\\\\\\mapsto\sf{A=320\cancel{00}\times \dfrac{81}{8\cancel{0}} \times \dfrac{81}{8\cancel{0}} }\\\\\\\mapsto\sf{A=\cancel{320}\times \dfrac{81\times 81}{\cancel{64}} }\\\\\\\mapsto\sf{A=Rs.(5* 81*81)}$

$\mapsto\sf{\red{A=Rs.32805}}$

∴ The amount is Rs.32805 .

We know that Compound Interest :

$\leadsto\sf{C.I.=A\:-\:P}\\\\\leadsto\sf{C.I.=Rs.32805-Rs.32000}\\\\\leadsto\sf{\red{C.I.=Rs.805}}$

Thus,

The Compound Interest (C.I.) = Rs.805.

Answer 2

Answer:

AnswEr :

\bf{\red{\underline{\underline{\mathcal{GIVEN\::}}}}}

GIVEN:

Principal,[P] = Rs.32000

Rate,[R] = 5% per annum

Time,[n] = 6 months.

\bf{\red{\underline{\underline{\mathcal{TO\:FIND\::}}}}}

TOFIND:

The amount.

The compound Interest.

\bf{\red{\underline{\underline{\mathcal{EXPLANATION\::}}}}}

EXPLANATION:

Formula use : (For compounded quarterly).

A/q

Now;

\begin{lgathered}\mapsto\sf{A=32000\bigg(1+\dfrac{5}{4\times 100} \bigg)x^{\cancel{4}\times \dfrac{1}{\cancel{2}} }} \\\\\\\mapsto\sf{A=32000\bigg(1+\cancel{\dfrac{5}{400}} \bigg)^{2} }\\\\\\\mapsto\sf{A=32000\bigg(1+\dfrac{1}{80} \bigg)^{2} }\\\\\\\mapsto\sf{A=32000\bigg(\dfrac{80+1}{80} \bigg)^{2} }\\\\\\\mapsto\sf{A=320\cancel{00}\times \dfrac{81}{8\cancel{0}} \times \dfrac{81}{8\cancel{0}} }\\\\\\\mapsto\sf{A=\cancel{320}\times \dfrac{81\times 81}{\cancel{64}} }\\\\\\\mapsto\sf{A=Rs.(5* 81*81)}\end{lgathered}

↦A=32000(1+

4×100

5

)x

4

×

2

1

↦A=32000(1+

400

5

)

2

↦A=32000(1+

80

1

)

2

↦A=32000(

80

80+1

)

2

↦A=320

00

×

8

0

81

×

8

0

81

↦A=

320

×

64

81×81

↦A=Rs.(5∗81∗81)

\mapsto\sf{\red{A=Rs.32805}}↦A=Rs.32805

∴ The amount is Rs.32805 .

We know that Compound Interest :

\begin{lgathered}\leadsto\sf{C.I.=A\:-\:P}\\\\\leadsto\sf{C.I.=Rs.32805-Rs.32000}\\\\\leadsto\sf{\red{C.I.=Rs.805}}\end{lgathered}

⇝C.I.=A−P

⇝C.I.=Rs.32805−Rs.32000

⇝C.I.=Rs.805

Thus,

The Compound Interest (C.I.) = Rs.805.