Question

Find the compound interest on Rs. 10000
for 3yrs at 5% p.a?
Select one:
a. 1576
b. 1500
c. 10000
d. 1543​

Answer 1

Given:

• Rs.10000 is conpounded for 3years at 5% p.a

To Find:

• The compound interest on the money.

Solution:

★ We know,

$\: \: \: \: \: \: \: \: \: \: \dag \bigg[ \bf \: A = P(1 + \frac{r}{100} ) {}^{n} \bigg]$

★ Where,

• A stands for amount
• P stands for principal
• R stands for rate of interest
• N stands for time

★ Here,

• principal = 10000
• Rate = 5%
• Time = 3 years

${ \underline{ \bf{ \bigstar \: substituting \: the \: values \: we \: get : }}}$

$\\{ : \implies}\bigg[ \bf \: A = P(1 + \frac{r}{100} ) {}^{n} \bigg] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}\bigg[ \bf \: A = 10000(1 + \frac{5}{100} ) {}^{3} \bigg] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}\bigg[ \bf \: A = 10000( \frac{100}{100} + \frac{5}{100} ) {}^{3} \bigg] \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}\bigg[ \bf \: A = 10000( \frac{105}{100} ) {}^{3} \bigg] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies}\bigg[ \bf \: A = 10000 \times \frac{105}{100} \times \frac{105}{100} \times \frac{105}{100} \bigg] \\ \\ \\ { : \implies} \bf \: A = 105 \times 105 \times \frac{105}{100} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf A = \frac{1157625}{100} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \bf { \underline{ \boxed{ \pmb{ \frak{A = 11576.25}}}} \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the amount is Rs.11576.25

★ We know,

$\: \: \: \: \: \: \: \: \: \: \dag \bigg[ \bf \: compund \: intrest = A - P\bigg]$

★ Here,

• Amount = 11576.25
• Principal = 10000

★ Substituting we get,

➼ C.I = A - P

➼ C.I = 11576.25 - 1000

➼ C.I = 1576.25

• When rounded you get,

➱ C.I = Rs.1576

Hence,

• option ( a ) Rs. 1576 is correct

More to know:-

• Formula to find amount when compounded half yearly

${ : \implies}\bigg[ \bf \: A = P(1 + \frac{r}{200} ) {}^{2n} \bigg]$

• Formula to find amount when compounded quarterly

${ : \implies}\bigg[ \bf \: A = P(1 + \frac{r}{400} ) {}^{3n} \bigg]$

• Formula to find amount at different rate of intrests

${ : \implies}\bf \: A = P \bigg[1 + \frac{ r_{1} }{100} \bigg]\bigg[1 + \frac{ r_{2} }{100} \bigg]\bigg[1 + \frac{ r_{3} }{100} \bigg]$

Answer 2

Given :

• Principal (P) = Rs 10000
• Time (n) = 3 years
• Rate (R) = 5% per annum

To Find :

• Compound interest

Formulas :

$\red \bigstar \: {\underline{\boxed{\mathcal {\pmb{\quad Amount \: = \: Principal \: \times \bigg(\:1 \: + \: \dfrac{Rate}{100}\bigg)^{n}\quad}}}}}$

$\red \bigstar \: {\underline{\boxed{\mathcal {\pmb{\quad Compound \: Interest \: = \: Amount \: - \: Principal \quad}}}}}$

Solution :

${:} \longrightarrow \sf \: Amount \: = \: Principal \: \times \bigg(\:1 \: + \: \dfrac{Rate}{100}\bigg)^{n} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 10000 \: \times \bigg(\:1 \: + \: \dfrac{5}{100}\bigg)^{3} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 10000 \: \times \bigg(\dfrac{105}{100}\bigg)^{3} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 10000\: \times \: \dfrac{105}{100} \: \times \: \dfrac{105}{100} \: \times \: \dfrac{105}{100} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 1\cancel{0000} \: \times \: \dfrac{105}{1 \cancel{00}} \: \times \: \dfrac{105}{1 \cancel{00}} \: \times \: \dfrac{105}{100} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: \dfrac{ 105 \: \times \: 105 \: \times \: 105}{100} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: \dfrac{105 \: \times \: 11025}{ 100} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: \dfrac{1157625}{ 100} \\ \\ {:} \longrightarrow \underline{\boxed{\sf \: Amount \: = \: Rs \: 11576.25}} \: \blue \bigstar$

________________

$\longmapsto {\pmb{ Compound \: Interest \: = \: Amount \: - \: Principal} } \\ \\ \longmapsto {\sf{ Compound \: Interest \: = \: 11576.25 \: - \: 10000} } \\ \\ \longmapsto \underline{\boxed{\pmb{ \red{ Compound \: Interest \: = \:Rs \:1,576.25} }}}$

________________

$\qquad \therefore\: \sf{ Amount \: = \underline {\underline{ Rs \: 11576.25}}}$

$\qquad \therefore\: \sf{ Compound \: Interest\: = \underline {\underline{ Rs \: 1,576.25}}}$

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