Question

1. Calculate the amount and compound interest on
(1) 15000 for 2 years at 10% per annum compounded annually
(ii) ? 156250 for 1 years at 8% per annum compounded half yearly
(ii) 100000 for 9 months at 4% per annum compounded quarterly​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Amount=18150\:rupees}}}$

$\green{\tt{\therefore{Compound\:Interest=3150\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt:\implies Principal(p) = 15000\:rupees \\ \\ \tt:\implies Rate\%(r)= 10\% \\ \\ \tt:\implies Time(t) = 2 \: years \\ \\ \red{\underline \bold{To \: Find : }} \\ \tt: \implies Amount =? \\ \\ \tt: \implies Compound \: Interest =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies A = p(1 + \frac{r}{100} )^{t} \\ \\ \tt: \implies A =15000 \times (1 + \frac{10}{100} )^{2} \\ \\ \tt: \implies A =15000 \times (1 + 0.1)^{2} \\ \\ \tt: \implies A =15000 \times 1.1^{2} \\ \\ \tt: \implies A =15000 \times 1.21 \\ \\ \green{\tt: \implies A =18150 \: rupees} \\ \\ \bold{For \: Compound \: Interest : } \\ \tt: \implies C.I=A - p \\ \\ \tt: \implies C.I=18150 - 15000 \\ \\ \green{\tt: \implies C.I=3150 \: rupees}$

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Amount=169000\:rupees}}}$

$\green{\tt{\therefore{Compound\:Interest=12750\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt:\implies Principal(p) = 156250\:rupees\\ \\ \tt:\implies Rate\%(r)= 8\% \\ \\ \tt:\implies Time(t) = 1\: years \\ \\ \red{\underline \bold{To \: Find : }} \\ \tt: \implies Amount = ? \\ \\ \tt: \implies Compound \: Interest =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies A = p(1 + \frac{ \frac{r}{2} }{100} )^{2t} \\ \\ \tt: \implies A=156250 \times (1 + \frac{8}{2 \times 100} )^{2} \\ \\ \tt: \implies A=156250 \times (1 + 0.04)^{2} \\ \\ \tt: \implies A =156250 \times 1.04^{2} \\ \\ \tt: \implies A=156250 \times 1.0816 \\ \\ \green{\tt: \implies A =169000 \: rupees} \\ \\ \bold{For \: Compound \: Interest : } \\ \tt: \implies C.I =A - p \\ \\ \tt: \implies C.I=169000- 156250 \\ \\ \green{\tt: \implies C.I =12750 \: rupees}$

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Amount=103030.1\:rupees}}}$

$\green{\tt{\therefore{Compound\:Interest=3030.1\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt:\implies Principal(p) = 100000\:rupees\\ \\ \tt:\implies Rate\%(r)= 4\% \\ \\ \tt:\implies Time(t) = 9 \: month \\ \\ \red{\underline \bold{To \: Find : }} \\ \tt: \implies Amount =? \\ \\ \tt: \implies Compound \: Interest =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies A= p(1 + \frac{ \frac{r}{4} }{100} )^{4t} \\ \\ \tt: \implies A =100000 \times (1 + \frac{4}{4 \times 100} )^{3} \\ \\ \tt: \implies A =100000 \times (1 + 0.01 )^{3} \\ \\ \tt: \implies A=100000 \times 1.01^{3} \\ \\ \tt: \implies A =100000 \times 1.030301 \\ \\ \green{\tt: \implies A = 103030.1 \: rupees} \\ \\ \bold{For \: Compound \: Interest : } \\ \tt: \implies C.I =A - p \\ \\ \tt: \implies C.I=103030.1- 100000 \\ \\ \green{\tt: \implies C.I =3030.1 \: rupees}$

Answer 2

$\huge{\mathfrak{Question}}$

(i) Given,

Principal = 15000

Rate = 10%

Time = 2 years

Therefore, finding Amount and Compound Intrest

$=> A = p(1 + \frac{r}{100} ) ^{t}$

$=> A = 15000(1 + \frac{10}{100} )^{2}$

$= > A = 15000 (1 + \frac{1}{10} ) ^{2}$

$= > A = ( \frac{10 + 1}{10} ) ^{2}$

$= > A = 15000 \times ( \frac{11}){10} ^{2}$

$= > A = 15000 \times {(1.1)}^{2}$

$= > A = 15000 \times 1.21$

Therefore, $A = 18150$

To calculate CI,

CI = A - P

CI = 18150 - 15000

CI = 3150

$\huge\pink{\mathfrak{Answer}}$

A = 18150

CI = 3150

(ii) Given,

Principal = 156250

Rate = 8%

Time = 1 years

Therefore, finding Amount and Compound Intrest.

$=> A = p(1 + \frac{r}{100} ) ^{t}$

$= > A = 156250(1 + \frac{ \frac{r}{2} }{100} )^{2t}$

$= > A = (1 + \frac{8}{2 \times 100} ) ^{2}$

$= > A = 156250 (1 + \frac{8}{200} ) ^{2}$

$= > A = 156250( \frac{200 +8 }{200}) ^{2}$

$= > A = 1562500 \times \frac{208}{200} \times \frac{208}{200}$

$= > A = 169000$

Therefore, $A = 169000$

To calculate CI,

CI = A - P

CI = 169000 - 156250

CI = 12750

$\huge\green{\mathfrak{Answer}}$

A = 169000

CI = 12750

(iii) Given,

Principal = 100000

Rate = 4%

Time = 9 months

Therefore, finding Amount and Compound Intrest.

$=> A = p(1 + \frac{r}{100} ) ^{t}$

$= > A = p(1 + \frac{ \frac{r}{4} }{100} )^{4t}$

$= > A = 100000(1 + \frac{4}{4 \times 100} )^{3}$

$= > A = 100000(1 + \frac{4}{400} ) ^ {3}$

$= > A = 100000 ( 1+ \frac{400}{4} ) ^{3}$

$= > A = 100000(1 + \frac{1}{100} )^{3}$

$= > A = 100000(1 + \frac{1}{100} ) ^{3}$

$= > A = 100000( \frac{100 + 1}{100})^{3}$

$= > A = 100000 \times \frac{101}{100} \times \frac{101}{100} \times \frac{101}{100}$

$= > A = 10000 \times 1.01 \times 1.01 \times 1.01 \\ = > A = 100000 \times 1.030301 \\ = > A = 103030.1$

$= > A = 103030.1$

Therefore, $A = 103030.1$

To calculate CI,

CI = A - P

CI = 103030.1 - 100000

CI = 3030.1

$\huge\blue{\mathfrak{Answer}}$

A = 103030.1

CI = 3030.1

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